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https://archive.org/details/elementarytreati01wils 


LOLi. 


O 


AN 


ELEMENTARY  TREATISE 


LOGIC; 

INCLUDING 

PAST  I.  ANALYSIS  OF  FORMULA-PART  II.  METHOD. 


WITH  AN 

APPENDIX  OP  EXAMPLES 


DESIGNED  FOR  THE  USE  OF  SCHOOLS  AND  COLLEGES  AS  WELL  AS  FOR  PRIVATE 
STUDY  AND  USE. 


BY 

W.  D.  WILSON,  D.  D., 

TRINITY  PROFESSOR  OF  CHRISTIAN  ETHICS,  AND  PROFESSOR  OF  LOGIC,  OF  INTELLECTUAI 
PHILOSOPHY,  AND  OF  HISTORY  IN  HOBAET  FREE  COLLEGE, 

AT  GENEVA,  WESTERN  NEW  YORK. 


Logic — the  Mathematics  of  Thought.” — Cousin. 


NEW  YORK : 

D.  APPLETON  AND  COMPANY, 

346  & 34S  BBO  AD  WAT. 

LONDON:  16  LITTLE  BRITAIN. 

M.DCCC.LVI. 


Entered  according  to  Act  of  Congress,  in  the  year  1856, 


By  D.  APPLETON  & COMPANY, 

In  the  Clerk’s  Office  of  the  District  Court  of  the  United  States  for  the  Southern 
District  of  New  York. 


The  following  work  has  grown  out  of  my  necessities  and 
my  experience  as  a teacher.  When,  several  years  ago,  I 
accepted  a professorship,  the  duties  of  which  required  me  to 
teach  Log-ic,  I could  nowhere  find  a text-hook  that  seemed  to 
me  to  satisfy  the  demands  of  the  science. 

Nor  was  this  feeling  peculiar  to  myself.  Mr.  Thompson, 
in  his  excellent  work  on  “ The  Necessary  Laws  of  Thought ,” 
begins  his  preface  with  saying : “ The  system  of  pure  Logic,  or 
analytic  that  has  been  universally  accepted  for  centuries  past, 
is  very  defective  as  an  instrument  for  the  analysis  of  natural 
reasoning.  Arguments  that  commend  themselves  to  any  un- 
taught mind  as  valid  and  practically  important,  have  no  place 
in  a system  that  professedly  includes  all  reasoning  whatever ; 
and  an  attempt  to  reduce  to  its  technical  forms  the  first  few 
pages  of  any  scientific  work,  has  generally  ended  in  failure 
and  disgust.” 

It  would  not  be  difficult  to  produce  almost  any  amount  of 
testimony  to  the  prevalence  of  a similar  feeling  with  regard  to 
the  present  state  of  literature  in  this  department  of  science 
and  instruction. 

Of  all  the  efforts  which  have  recently  been  made  to  remedy 
this  deficiency,  two  can  be  considered  as  requiring  notice  in 
this  place : that  of  Prof.  De  Morgan,  and  that  of  Sir  Wil- 


250436 


IV 


PREFACE. 


liam  Hamilton.  The  work  of  Mr.  Thompson  just  referred 
to,  is,  in  its  essential  features,  little,  if  any  thing,  more  than  an 
exposition  of  Sir  William’s  theory. 

Prof.  De  Morgan  has  earned  a name  in  his  own  depart- 
ment (mathematics),  which  scholars  hereafter  will  he  pleased 
to  remember  and  contemplate.  But  philosophy,  in  any  of  its 
departments,  is  not  his  calling.  His  theory  is  essentially  nu- 
merical. He  measures  every  thing  by  numerical  quantity 
rather  than  logical.  For  the  purposes  of  calculation,  2X,  X, 
and  X2  are  truly  different  terms,  and  can  no  more  be  substi- 
tuted for  each  other  than  X,  Y and  Z.  In  this  case,  X,  Y and 
Z,  2 X and  X2,  are  assumed  as  representing  simply  num- 
ber ; that  is,  a number  of  units.  Now,  units  have  no  indi- 
vidual properties — nothing  to  distinguish  one  from  another. 
Much  less  have  they  any  separable  accidents ; and  the  only 
difference,  therefore,  between  the  sums  for  which  X,  Y,  Z,  &c., 
stand,  is  in  the  number  of  units  comprehended  in  each  sum, 
and,  consequently,  2 X and  X — the  one  being  twice  as  much 
as  the  other — are  no  more  the  same  than  X and  Y,  when  they 
represent  those  different  quantities. 

But  the  words  or  symbols  used  in  Logic  represent  the 
conceptions  that  we  form  of  objects  of  thought,  which  are  not 
units  merely,  but  individuals  also,  having  each  of  them  insep- 
arable and  peculiar  properties  of  their  own,  upon  which  not 
only  their  adequate  conception,  but  any  use  which  we  can 
make  of  that  conception  in  the  Formula,  whether  of  mediate 
or  of  immediate  deduction,  depends.  This  fact  has  been  over- 
looked in  Prof.  De  Morgan’s  Formal  Logic,  to  an  extent 
which  deprives  it  of  any  great  value  as  a system. 

Perhaps  the  best  test  of  any  theory,  is  a comparison  of  its 
deductions  with  the  obvious  facts  and  first  principles  of  know- 
ledge. De  Morgan  refers  to  an  anecdote  told  of  Zerah  Col- 
burn, which  relates,  that  having  been  asked  how  many  black 
beans  would  make  ten  white  ones,  he  replied — “ ten  if  you 


PREFACE. 


V 


skin  'em l”  “But,”  adds  De  Morgan,  “the  ten  skinned 
beans  would  not  he  the  same  beans  as  before — except,  indeed, 
to  those  to  whom  black  is  white.” — (p.  54  Formal  Logic.] 

In  the  common  sense  of  mankind,  the  beans  are  the  same 
after  being  skinned.  Philosophy  may  undertake  to  correct 
the  common  sense  notions  of  mankind,  but  Logic  cannot.  And 
with  how  much  success  philosophy  can  pursue  such  an  attempt 
we  will  not  now  undertake  to  decide.  But  in  this  case  it  can- 
not succeed.  The  conclusion,  if  established,  would  be  gener- 
alized at  once — as  in  fact  it  ought  to  be — and  we  should  have 
the  doctrine  that  identity  depends  upon  the  separable  accidents ; 
and  then  all  science,  all  knowledge,  ethics,  and  religion,  too,  will 
be  afloat  and  dissolved  into  fragments.  A man’s  separable  acci- 
dents change  from  day  to  day ; consequently  his  identity 
changes.  He  is  not  the  same  man  to-day  that  he  was  yesterday 
— is  not  bound  to  fulfil  the  contracts  of  yesterday,  or  to  suffer 
the  penalty  due  to  its  transgression. 

A theory  that  not  only  gives  such  results,  but  openly  avows 
them,  may  be  safely  considered  ab  absurdo. 

I cannot  but  regard  Sir  William  Hamilton’s  theory  as 
equally  unfounded. 

Sir  William’s  name  is  one  of  the  greatest  of  the  present 
century  of  great  names  in  philosophy.  His  rank  will  undoubt- 
edly be  in  the  first  class — with  Aristotle,  Plato,  Descartes, 
Locke,  and  Cousin — the  few  great  names  that  stud  the  galaxy 
of  history.  For  an  acquaintance  with  the  learning  and  works 
of  others  in  the  department  of  speculative  philosophy,  he  stands 
unrivalled,  and  probably  will  never  be  surpassed.  But  I have 
not  been  able  to  form  any  such  high  estimate  of  his  attempts 
at  originality. 

He  assumes  that  there  may  be  affirmative  judgments  with 
distributed  predicates.  This  is  so.  But,  as  I have  showr 
(Part  I,  chap.  II,  sec.  3. — See  also  p.  05,  § 244),  this  is  nevei 
done  by  the  mere  force  of  the  affirmative  copula.  The  fact,  if 


VI 


PREFACE. 


fact  it  be,  in  any  case,  must  always  be  indicated  by  something 
not  essential  to  the  judgment,  and  I have  provided  for  all  such 
cases — (p.  124,  §498 — see  456). 

But,  again,  he  assumes  that  there  may  be  negative  judg- 
ments with  undistributed  predicates.  To  this  I have  given 
what  I think  will  be  found  a sufficient  answer  in  p.  67  § 254 
and  the  note.  A subject  is  excluded  from  a Predicate  only 
because  it  has  not  the  Essentia  of  the  class-conception  denoted 
by  that  predicate.  But  the  Essentia  of  one  part  of  the  individ- 
uals contained  in  it,  can  never  be  different  from  that  of  another. 
Hence,  whatever  would  exclude  a subject  from  a part  of  the 
predicate — that  is,  the  predicate  as  an  undistributed  term — 
would  exclude  it  for  the  whole  of  the  predicate  as  a distributed 
term. 

If  Sir  William’s  theories  were  correct  on  these  points, 
doubtless  we  should  be  obliged  to  abandon  the  old  nomencla- 
ture altogether  and  begin  anew;  as,  indeed,  Sir  William  pro- 
poses to  do.  But  believing  as  I do,  and  for  the  reasons  given, 
that  his  theory  of  quantification  is  fundamentally  wrong,  I 
have  adhered  to  the  old  doctrine,  so  modifying  the  statement 
and  exposition  of  it  as  to  provide  for  the  cases  which  he  had 
regarded  as  demanding  the  new  theory. 

It  will  also  be  observed,  that  in  the  following  treatise  I 
have  made  more  account  of  Method  than  recent  writers  have 
been  generally  inclined  to  do.  Many  of  them,  in  fact,  have 
omitted  it  entirely.  Perhaps  the  manner  in  which  it  had 
been  treated  by  the  scholastic  writers,  may  serve,  in  some 
measure,  as  a justification  for  the  estimate  in  which  the  modern 
authors  have  held  that  part  of  Logical  Science.  But  not  only 
is  it  of  the  utmost  importance  in  itself ; there  is,  moreover,  as 
I conceive,  no  way  of  obviating  the  objection  to  devoting  so 
much  time  as  is  requisite  to  the  mastery  of  what  Whately  and 
others  with  him  who  omit  method  altogether,  have  included 
in  their  treatises,  without  revising  that  part  of  Logic  which  is 


properly  denoted  by  the  word  Method,  and  in  thus  giving 
practical  direction  and  applicability  to  the  whole  study.  This 
is  what  I have  attempted  to  do  in  the  part  on  Method,  and  I 
hope  that  scholars  and  teachers  will  agree  with  me  in  the  esti 
mate  I have  placed  upon  the  subject. 

If  Logic  is  as  Cousin  has  remarked,  “ the  Mathematics  of 
thought,”  it  must  comprehend  not  only  an  analysis  of  the  For- 
mula which  we  use  in  thinking,  hut  also  the  methods  of  the 
successful  application  of  these  Formulae,  and  the  discussion  of 
Methods  will  require  some  consideration  of  the  Matter  to 
which  they  are  to  he  applied,  and  the  faculties  by  which  we 
apply  them. 

As  the  Analytic  of  Formulae  may  be  compared  to  Geometry, 
so  Method  may  with  equal  propriety  be  compared  to  Arith- 
metic, Algebra,  and  the  Calculus  in  pure  Mathematics — the 
former  treats  of  Form  in  Space,  considered  simply  as  continu- 
ous quantity;  the  latter  of  methods  of  finding  results  in  dis- 
crete quantity.  Such  Methods  are  not  only  Addition,  Sub- 
traction, Multiplication  and  Division,  Involution  and  Evolu- 
tion, but  also  the  Binomial  Theorem,  the  system  of  Indetermi- 
nate Coefficients,  and  all  the  Methods,  in  short,  of  Differentia- 
tion and  Integration.  Every  mathematician  knows  that  the 
truth  of  the  result  depends  upon  two  conditions,  (1.)  that  the 
Method  be  applied  to  proper  matter ; and  (2.)  that  the  Methods 
themselves  are  legitimate. 


I have  also  provided  in  the  Appendix  a liberal  supply  of 
examples  for  Praxis.  These  examples  may  not  be  sufficient 
to  illustrate  every  principle  and  formula,  as,  from  the  necessities 
of  the  case,  they  are  for  the  most  part  ultimate  parts  in  them- 
selves, and  do  not  admit  of  the  application  of  some  of  those  prin- 
ciples which  relate  to  the  construction  of  more  comprehensive 
wholes.  Our  limits  will  not  allow  of  the  insertion  of  examples 
illustrative  of  some  of  the  principles  of  Method  which  we  have 
described.  Such  examples  can  be  found  only  in  the  books  and 


vni 


PREFACE. 


treatises  which  are  altogether  too  long  to  he  reprinted  here 
Nor  can  they  be  represented  in  any  brief  or  abstract,  in  such 
a way  as  to  test  the  principle  or  be  of  use  in  criticising  the 
examples  themselves. 

I have  also  divided  these  examples  into  classes,  so  that,  if 
thought  best,  they  may  be  used  as  the  student  progresses  in 
the  Analysis  of  Formulae — the  first  four  sections  being  arranged 
with  a view  to  corresponding  divisions  of  Part  I.  of  this  work. 

Among  the  many  analogies  between  Logic  and  Grammar, 
no  one  is  more  important  and  striking  than  that  property  in 
common  from  which  it  results ; that  as  iu  the  one  case,  so  in  the 
other,  there  is  scarcely  the  possibility  of  getting  a thorough 
kuowledge  of  principles  and  formula  without  much  experience 
in  what  in  Grammar  we  call  parsing.  This  practice  in  Logic 
has  come  to  be  called  Praxis.  It  consists  in  a careful  analysis 
of  all  argumentative  sentences  with  reference  to  the  logical 
connection  and  sequence  of  the  judgments  which  they  express, 
the  methods  of  argumentation,  and  the  adaptation  of  the 
Methods  to  the  matter. 

But  the  very  process  by  which  we  thus  perfect  our  know- 
ledge of  the  Principles  and  Formulas  into  familiarity  with  their 
use,  is  precisely  that  which  we  are  obliged  to  practise  in  all 
cases  where  we  apply  our  Logic  at  all  in  the  purposes  and  uses 
of  life.  Praxis  only  makes  perfect  in  the  art  of  using  our 
faculties  and  our  knowledge  in  the  wider' and  more  important 
spheres  for  which  our  studies  are  designed  to  fit  us. 

It  is,  I believe,  owing  to  the  neglect  of  Praxis,  together 
with  the  practical  difficulty  (which  nothing  but  much  practice 
can  remove)  of  putting  propositions  into  a Formal  shape,  that 
the  impression  that  a large  part  of  the  arguments  in  every  book 
to  which  the  mind  assents,  cannot,  nevertheless,  be  put  into 
any  one  of  the  known  and  recognized  Formulae,  has  become  so 
general. 

Language  seldom  expresses  all  that  is  in  the  thoughts,  and 


PREFACE. 


IX 


still  more  seldom  all  that  is  implied  in  what  is  actually  said. 
Rules  of  rhetoric  and  taste  would  forbid  such  prolixity,  even  if 
it  were  possible.  But  Logic  supposes  nothing.  It  demands 
that  all  that  is  in  the  thought  should  be  fully  and  explicitly 
stated.  And  one  who  has  given  a thorough  logical  analysis  to 
any  production,  must  of  necessity  understand  it  as  well  as  he 
who  wrote  it,  and  probably,  in  nine  cases  out  of  ten  at  least,  he 
would  really  understand  it  much  better.  He  must  understand  it 
thoroughly , which  is  certainly  more  than  can  in  all  cases  with 
propriety  be  said  of  the  author  himself.  How  many  Enthy- 
memes  are  uttered,  the  suppressed  premises  of  which  are  wholly 
unknown  and  unsuspected  to  him  who  expresses  the  Enthy- 
meme  ? How  many  conditionals,  the  sequences  of  which  are  un- 
known to  the  writer  or  speaker  himself?  But  all  the  latent 
elements  of  these  imperfect  arguments  must  have  been  brought 
out,  stated,  and  examined  by  him  who  has  gone  through  with 
a thorough  logical  criticism  of  the  production. 

The  student  and  the  teacher  likewise  will  probably  find  the 
chapter  on  Methods  of  instruction  the  least  full  and  satisfac- 
tory of  any.  The  reason  for  this  is  assigned  in  the  chapter 
itself.  I could  not  make  it  full  and  satisfactory  without  going 
further  than  unity  of  plan  would  permit  into  the  department  of 
Rhetoric,  nor  (waiving  that  objection),  could  I go  into  the 
subject  so  fully  as  such  a modification  of  my  general  subject 
would  require,  without  expanding  the  volume  beyond  all  reason- 
able bounds.  And,  after  much  deliberation,  I have  decided  to 
send  it  out  as  it  is,  regarding  it  as  the  best  that  I can  make 
of  the  matter  now  and  under  the  present  circumstances.  Such 
as  it  is,  however,  I trust  that  it  will  not  be  found  unworthy 
of  attention  and  diligent  study. 

In  conclusion,  I wish  to  express  my  decided  conviction 
not  only  of  the  usefulness  of  Logic  as  an  instrument,  but  also 
that  it  needs  more  attention  and  more  time  than  any  work  on 
the  subject  hitherto  given  to  the  public,  has  seemed  to  me  to 


X 


PREFACE. 


deserve.  It  is  to  all  the  speculative  sciences,  every  branch  of 
knowledge  except  mathematics,  what  arithmetic  and  algebra 
are  to  the  Mathematics  themselves — as  an  instrument  in  con- 
structing those  sciences — and  it  is  as  necessary  as  grammar  it- 
self to  rhetoric,  and  all  the  departments  of  literary  criticism, 
dialectics,  and  oratory. 

In  speaking  thus  of  the  importance  of  the  science,  and  of 
a thorough  education  in  it,  I am  not  of  course  advocating  the 
introduction  of  its  technicalities  and  Formulae  into  public  speak- 
ing and  writing ; the  analogy  of  grammar  and  rhetoric  holds 
here  also.  No  one,  in  speaking  or  writing,  stops  to  parse  his 
words,  or  to  name  every  figure  of  speech  which  he  uses,  or  every 
rule  of  rhetoric  which  he  may  have  had  in  mind  when  he  wrote 
or  spoke.  No  more  is  it  expected  that  the  same  thing  should 
be  done  in  regard  to  Logic.  Here,  as  elsewhere,  it  may  be 
said,  the  greatest  art  is  to  conceal  art — to  write  with  a perfect 
knowledge  of  all  the  terms  and  principles  of  the  science  of 
writing,  and  yet  never  thrust  them  forward  in  such  a way  as  to 
be  offensive  to  good  taste,  or  vexatious  to  the  reader. 

To  reason  logically  is  not  the  same  as  to  reason  formally. 
All  good  reasoning  is  of  necessity  logical,  just  as  all  good  writ- 
ing must  fulfil  the  rules  and  requirements  of  grammar  and 
rhetoric.  But  it  is  not  expected  that  the  arguments  will 
always  be  stated  in  the  precise  forms  that  are  given  in  this 
book;  nor  that  all  that  is  requisite  to  their  completion  shall 
be  expressly  given.  Logic  supposes  nothing.  It  allows  of  no 
omissions — no  ellipses.  On  the  contrary,  rhetoric,  good  taste, 
brevity,  and  more  than  all,  the  scantiness  of  thought  in  the  mind 
of  the  speaker,  make  this  necessary.  Logic  teaches  what  these 
omissions  are,  how  they  are  to  be  restored  or  produced  to 
fill  up  the  vacancies.  And  thus  the  reasoning  fulfils  the  For- 
mula— becomes  formal — or,  as  it  is  commonly  but  very  impro- 
perly called,  logical.  But  nothing  can  be  more  idle  than  the 
objection  to  the  study  of  Logic,  based  upon  the  fact  that  its 


PREFACE. 


XI 


Formulas  and  technicalities  do  not  appear,  and  are  not  expected 
to  appear,  in  the  written  or  published  discourse  of  ordinary 
life.  One  might  with  as  much  propriety  object  to  the  study 
of  the  Binomial  Theorem,  on  the  ground  that  in  equations  of 
the  second  degree,  we  seldom  or  never  find  the  square  of  the 
Binomial  complete.  Without  these  Formulae  and  technicalities, 
what  is  written  and  said  can  never  be  comprehended  or  intel- 
ligibly discussed. 

But,  after  all,  it  must  be  distinctly  considered  that  Logic, 
like  the  pure  Mathematics,  is  only  a means  and  not  an  end.  The 
pursuit  of  the  study  may  be  valuable  as  a discipline.  Its 
results  will  be  of  great  service  to  any  one  who  has  thoroughly 
comprehended  them.  But  if  one  looks  to  its  Formulae  as  a 
substitute  for  common  sense  in  the  common  affairs  of  life,  or 
of  investigation  in  the  higher  pursuits  of  literature  and  science, 
or  of  patient  and  laborious  thought  anywhere,  he  will  be  sadly 
disappointed. 

W.  D.  WILSON. 

Geneva,  Dec.,  1855. 


CONTENTS. 


PAGE 

Introduction. — Logic  Defined ; its  Origin,  Necessity,  and  Uses ; its 
Sphere  Pointed  out,  and  the  Starting  Point  Ascer- 
tained,  1 


PART  I. 

ANALYSIS  OF  FORMULAE. 

CHAPTER  I. 

OF  TERMS. 

Section  I. — Of  Conceptions — their  Formation,  their  Object  and  Rela- 
tions,   9 

II. — Of  Substance  and  Properties • — Sphere  and  Matter  of  Con- 
ceptions, Essentia,  Genus,  General  and  Collective 
Terms,  Differentia  and  Species,  Individual  and  Acci- 
dents,   13 

III. — Of  the  whole  and  its  Parts , 21 

I. — Of  Quantity,  there  kinds, 22 

II. — Of  Division,  three  kinds, 24 


XIV 


CONTENTS. 


Sec.  IV. — The  Relation  of  Cause  and  Effect, 29 

V- — Of  Difference,  Identity,  Resemblance,  and  Analogy, 32 

VI. — Of  Definition  and  Description 33 

^ II-  Of  the  Quality  of  Terms — General,  Specific,  Synonymous, 
Analogous,  Incompatible,  Positive,  Negative,  and  Priva- 
te,   34 

VIII.  — Of  the  Quantity  of  fTerms — Numerals,  Ordinals,  Positive 

and  Negative,  Infinite,  Comparatives  and  Superlatives, 

Distributed  and  Undistributed, 38 

IV. — Of  the  Opposition  of  Terms — Relative,  Contrary,  Sub- 
contrary, Contradictory, 40 

CHAPTER  H. 

OF  PROPOSITIONS. 

Section  I. — Of  Judgments — Scope,  Kinds,  Categorical,  Conditional, 
Disjunctive,  Hypothetical,  Relative  or  Comparative,  and 
Probable, 43 

II. - — Of  the  Terms  in  a Proposition — how  Placed,  Propositions 

Resolvable  into  Terms, 46 

III.  — Of  the  Copula — its  Force,  Forms,  Effects,  and  Classifi- 

cation,   48 

IV.  — Of  the  Adequacy  of  Propositions, 55 

V.  — Of  the  Quantity  of  Judgments — Individual,  Particular, 

and  Universal  Judgments, 59 

VI. —  Of  the  Quality  of  Judgments, 61 

VII.  — Of  the  Modality  of  Judgments, 61 

VIII. — Of  the  Pour  Cardinal  Propositions — Universal  Affirma- 
tive, Universal  Negative,  Particular  Affirmative,  and 
Particular  Negative, 62 

IX. —  Of  the  Distribution  of  Terms  in  Judgments, 64 

X. — Of  Immediate  Inference, 69 

I. — By  tiie  Opposition  of  Judgments, 70 

II. — By  Permutation  or  Contra- Position, 71 

III.  By  Conversion, 74 

IV.  — By  Substitution  of  Teems, 76 


CONTENTS. 


XV 


PAGE 

Sec.  XI. — Of  Complex  Propositions — Modals,  Explicative,  Differ- 
ential, Exceptional,  Exclusive,  Conditional,  and  Pro- 
trusive,  77 

XII. — Of  Compound  Propositions- — Express  and  Implied,  Copu- 
lative Causal,  Discretive,  Conditional,  and  Disjunctive, 
Exceptives,  and  Exclusives, 80 

XIII.  — Of  Comparative  Judgments 84 

XIV.  — Of  Probable  Judgments — The  Calculation  of  Chances, 

Antecedent  and  Special  Probabilities, 87 

XV. — Of  Conditional  Judgments — The  Sequence,  Complex  Se- 
quences, Compound  and  Continuous  Conditionals, 91 

XVT. — Of  Disjunctive  Judgments  and  Excluded  Middle, 97 

XVII. — Of  the  Grounds  of  Affirmation — Identity  and  Contradic- 
tion, Sufficient  Cause,  and  Excluded  Middle 102 

CHAPTER  IIL 

OF  SYLLOGISMS. 

Section  I —Classification  of  Syllogisms — Names  of  the  Terms,  and 

Parts  in  Pure  Categorical  Syllogisms, 106 

n. — Of  Pure  Categorical  Syllogisms, 110 

X. — Of  the  Figure  of  Syllogisms, 110 

II. — Of  tiie  Moon  of  Syllogisms, 115 

III. — Application  of  Moons  to  tiie  Figures, 118 

III.  — Of  Indirect  Conclusions , 123 

IV.  — Of  the  Conversion  of  Syllogisms — Ostensive  Reduction, 

and  Reductio  ad  impossibile, 121 

V.  — Of  Complex  Syllogisms — Change  of  Modals  and  Proten- 

sive  Quantity, 131 

VI. — Of  Compound  Syllogisms,  or  Sorites,  the  Reduction  of 

Sorites  to  Simple  Categoricals, 138 

VII. — Of  the  Incomplete  Formulas,  or  Enthymemes,  Inductive 

and  Cumulative  Formula, 142 

Vni. — Of  Epichirema,  Pro-syllogisms,  and  Epi-syllogisms, 148 

IX. — Of  Compound  Judgments  in  Syllogisms , 149 


XVI 


CONTENTS. 


PAGE 

Sec.  X. — Of  Comparative  Syllogisms — 

I. — Simple  Comparatives, 152 

II. — Comparatives  in  irmcn  tiie  Difference  of  Intensity 

is  Regarded  as  a Cause, 155 

III. — Comparatives,  Manner,  &c., 156 

XI. — Of  Probable  Syllogisms,  the  Effect  of  Discrete  Quantity- 
on  Logical,  and  the  Combination  of  Independent  Pro- 
babilities,  157 

XII.  — Of  Conditional  Syllogisms — their  Completion, 170 

XIII.  — Of  Disjunctive  Syllogisms — Comprehensive  and  Divisive  175 

XIV.  — Of  the  Dilemma 179 

CHAPTER  IV. 

OF  FALLACIES. 

Section  I. — Of  the  Ig noratio  Elenchi, 185 

II. — Of  the  Petitio  Principii, 186 

in. — Of  the  Ambiguous  Middle, 189 

IV. — Of  Division  and  Composition, 190 

V. — Of  Accidents  and  Quid, 191 


PAKT  II. 

LOGICAL  METHODS. 

CHAPTER  I. 

of  the  elements  of  method. 

Section  I. — Of  Method  in  General 194 

II. — Of  Order  as  an  Element  of  Method, 196 

III. — Of  the  Ideas  which  Determine  Methods , 198 


CONTENTS. 


XVII 


PAGE 

Sec.  IV. — Of  the  Matter  of  Logical  Methods — Analytical  and  Syn- 
thetic Judgments,  Necessary  and  Contingent  Matter, 
Class-Conceptions,  Judgments  d priori  and  d posteriori. 
Material  and  Implied  Properties,  Formal  and  Modal 
Properties,  Absolute,  Physical,  and  Moral  Certainty, 
Analysis,  Synthesis,  Truth,  Opinion,  Hypothesis, 
Theory,  and  Conjecture, 202 

CHAPTER  n. 

METHODS  OF  INVESTIGATION. 

Section  I. — Of  Investigation — The  finding  of  Predicates, 219 

II. — Of  Observation  and  Testimony — the  External  Senses, 
Consciousness,  Experiment,  the  use  of  Hypotheses,  and 

of  Testimony, 

ni. — Of  Measurement  and  Calculation — Methods  of  Obtain- 
ing Wholes  from  Parts  and  Parts  from  Wholes, 232 

IV. — Of  Average  and  Exclusion,  or  the  Abscissio  Infniti, 237 

V. — Of  Analysis — The  Analysis  of  Conceptions  and  of  Ob- 
jects,   243 

VI. — Of  Induction  and  Analogy — Several  forms  of  Induction,  249 

VII. — Of  Elimination,  Causes  and  Antecedents — Causality  Im- 
plies Substance,  Methods  of  Elimination, 259 

CHAPTER  III. 

METHODS  OF  PROOF  AND  REFUTATON. 

Section  I. — Of  Proof — Direct  and  Indirect  Methods,.- 275 

II. — Of  Demonstration, 281 

III. — Of  Deduction, 290 

TV. — Of  the  Argument  from  Authority — Principles  of  Inter- 
pretation,  293 

V. — Of  the  Appeal  to  Facts,  by  way  of  Induction,  the  Uni- 
formity of  Nature,  Final  Causes,  Example,  Analogy, 
and  Circumstantial  Facts, 303 


XV111 


CONTENTS. 


PAGE 

Sec.  VI. — Of  Progressive  Approach, 324 

VII. — Of  the  Argumentum  ad  Ignorantiam, 326 

VIII. — Of  Refutation,  three  Methods 328 

IX. — Of  Direct  Refutation, 329 

X. — Of  Indirect  Refutation, 333 

XI. — Of  Personal  Refutations,  ad  hominem , ad  verecundiam, 

ad  invidiam, 336 

CHAPTER  IV. 

METHODS  OF  INSTRUCTION  AND  CRITICISM. 

Section  I. — Classification  of  the  Sciences — Plato’s  Classification, 
Aristotle’s  Scholastic,  Bacon’s,  Locke’s,  Ampere’s  and 

Compte’s — a new  one  proposed, 338 

H. — Of  the  Conveyance  of  Ideas  from  one  Mind  to  Another — 
as  Determining  Methods  of  Instruction,  Ideas  Con- 
veyed only  by  Definition  and  Reconstruction, 347 

III.  — Of  Definition  and  Description — Real  and  Verbal  Defini- 

tions, Definition  of  “ Simple  Ideas,”  Ultimate  Concep- 
tions, Description  Furnishes  no  Matter  for  a Concep- 
tion,   349 

IV.  — Of  Natural  and  Artificial  Classifications — Natural 

Classifications  made  in  Cognition,  Necessity  for  Scien- 
tific Classifications,  Recurring  Species, 356 

V. — Of  the  Division  of  the  General  Subject — Divisions  in  Pro- 

tensive  Extension,  in  Comprehensive, 360 

VI.  — Of  the  Order  in  the  Treatment — Matter  Divided  into 

Classes  with  Reference  to  the  Order  of  Statements,  Or- 
der Stated,  Rules  for  Omission  of  Matter  as  Irrelevant 
to  the  End  in  View,  Necessity  for  an  End  or  Special 
Aim, 361 

VII.  — Methods  of  Criticism — The  Critic’s  Point  of  View,  the 

Relation  of  Whole  and  Parts,  Argument  and  Impres- 
sion, Logical  Matter  and  mere  Assertion,  Arguments 
and  Artifices,  Criticism  of  Terms,  Contradictio  in  Ad- 
jectis,...., 369 


CONTENTS..  xix 

APPENDIX  OF  EXAMPLES  FOR  CRITICISM. 

§ 1.  Of  the  Order  in  Criticising  Arguments , 377 

§ 2.  Examples  in  Categorical  Syllogisms, 379 

§ 3.  Examples  in  Hypothetical  Syllogisms, 382 

§ 4.  Examples  in  Complete  and  Compound  Formulce, 386 

§ 5.  Miscellaneous  Examples  of  Formulce  and  Fallacies, 389 

§ 6.  Examples  Involving  Questions  of  Method, 396 

§ 7.  Leslie's  Short  and  Easy  Method, 401 

§ 8.  Webster's  Argument  in  the  Girard  Will  Case, 404 

§ 9.  Dana's  Argument  in  the  Ellsworth  School  Case, 407 

Index, 411 


LOGIC. 


INTRODUCTION. 

1.  The  word  Logic  has  been  used  in  many  different 
senses,  and  most  treatises  on  the  subject  have  LoeiP.  variou3. 
included  matter  belonging  to  widely  differ-  ly  defined- 
ent  spheres  of  thought  and  inquiry.  It  sometimes  de- 
notes the  science  which  explains  the  laws  of  thought 
merely.  It  is  sometimes  used  to  denote  the  art  of  con- 
vincing and  persuading.  It  has  been  thought  to  imply 
the  consideration  of  the  means  of  discovering  truth,  and 
also  the  general  principles  of  Method. 

2.  Philosophy  was  in  existence  and  cultivated  some 
time  before  Logic  appeared  as  a distinct  philosophy  be- 
Science  or  Art.  The  reason  is  obvious.  Men  fore  Logic- 
do  not  seek  a Canon  of  Truth  until  they  feel  the  danger 
of  error,  and  have  reaped  the  hitter  fruits  of  its  expe- 
rience. The  earliest  schools  of  Greek  Philosophy  (and 
of  the  Hindoo  Philosophy  we  cannot  now  speak,  for 
want  of  chronological  data)— the  Ionian  and  the  Pytha- 
gorean— argued  and  dogmatized  without  fear  or  expec- 
tation of  contradiction ; they  were  too  sanguine  and 
confident  to  feel  the  need  of  Logic. 

1 


2 


INTRODUCTION. 


3.  But  as  soon  as  the  doctrines  of  these  two  schools 
came  into  conflict,  some  Canon,  or  test,  of  truth  was  found 

The  origin  of  to  he  necessary.  Not  only  terms  in  which 
LoBic-  to  discuss  the  points  at  issue,  hut  an  in- 
spection of  first  principles,  and  of  the  processes  of 
deduction  from  them,  came  to  he  regarded  as  indis- 
pensable to  the  discovery  of  truth,  and  the  proper 
testing  of  the  means  by  which  it  may  be  proved  to  be 
true. 

4.  No  system  of  Logic,  however,  was  formally  de- 

veloped and  digested  until  Aristotle.  Aris- 
Author 0 of  the  totle  * himself,  however,  says  Zeno  the  Elea- 
rst^tem.  tic,  was  the  inventor  of  Logic,  or  rather 
Dialectics,  /haXe/cTiicr']. 

5.  As  soon,  however,  as  Philosophy  had  sufficiently 
explored  the  field  which  it  had  to  occupy,  to  form  any 
definite  idea  of  what  is  contained  in  it,  we  find  Plato 
dividing  it  into  three  coordinate  branches : — Physic, 

Threefold  i Ethic,  and  Logic  ; f — the  former  including 
vision^ Vhiio-  all  of  the  Natural  Sciences  ; the  second,  all 
that  concern  the  relations  and  duties  of  man  ; 
and  the  latter,  Logic,  the  science  of  mind,  and  the 
rules  by  which  its  activity  is  to  be  guided  to  the  proper 
results. 

6.  .Logic  is  derived  from  the  Greek  Aoyos,  and  in 
Logic,  how  the  sense  used  by  Plato,  it  means  whatever 

used  by  piato.  pertains  to  the  Mind,  the  Reason,  the  imma- 
terial power  or  faculty  which  is  manifested  in  the 
words  and  speech  of  men.  Logic  was  used  to  denote 
the  whole  of  what,  in  modern  times,  has  been  called 
Intellectual  Philosophy,  or  Metaphysics. 

7.  But  Intellectual  Philosophy  or  Metaphysics,  in 
this  broad  extent  of  meaning,  includes  at  least  three 
distinct  departments  of  science. 

(1.)  Psychology , as  it  is  called,  describing  the  facts 
of  the  mind,  of  which  we  are  immediately  conscious ; 

* Sext.  Empir.  adv.  Math.  B.  vii.  c.  1. 
f Diog.  Laert.,  Procem.  seg.  18. 


INTRODUCTION. 


3 


such  as  Sensation,  Perception,  Abstraction,  psychology. 
Conception,  Association,  Imagination,  Memory,  Intui- 
tion, Judgment,  Inference,  &c. 

(2.)  Metaphysics  proper,  which  investigates  the 
necessary  a priori  conditions  and  laws  of  Metaphysics, 
thought,  and  the  ideas  which  determine  cognition 
and  judgment,  and  those  necessary  axioms,  or  first 
principles,  which  are  assumed  in  all  sciences,  and 
underlie  them,  as  the  ground  of  their  possibility  and 
reality. 

And  (3.)  Logic ; which  treats  of  the  relations  of 
conceptions  to  one  another ; the  deduction  Logic  in  thi3 
of  secondary  from  primary  and  intuitive  narrowersen9e- 
judgments,  and  the  laws  of  Synthesis,  by  which  truths 
are  constructed  into  systems. 

8.  The  last  element  of  this  definition  is  what  has 
usually  been  called  Method  ; and  latterly  Methodnotm- 
there  has  been  a tendency  to  regard  it  as  a cluded  latterly- 
science  by  itself.  Excluding  Method,  therefore,  from 
our  definition,  Logic  may  he  defined  as  the  Science  of 
Deductive  Thinking. 

9.  As  there  may  be  true  and  legitimate  deductions 
as  well  as  such  as  are  false  and  delusive,  Logic  a Sci. 
there  must  be  a Science  of  deduction,  by  ence- 
which  the  true  may  be  distinguished  from  the  false ; 
and  the  laws  and  formulas  of  deduction  itself  so  ex- 
plained and  developed,  as  to  enable  one  to  select  and 
pursue  those  methods  which  lead  to  right  conclusions, 
and  avoid  those  that  are  fallacious. 

10.  But  it  is  necessary  for  the  practical  benefits  of 

the  science,  to  take  some  note  of  language,  Its  reIation  to 
or  the  words  and  signs  by  which  thinking  iecti4A?fRht- 
is  expressed  ; of  the  matter  of  which  we  torie- 
think  and  reason  ; and  especially  of  the  various  ways 
in  which  the  Formulae  may  be  used  in  the  construction 
of  what,  in  popular  language,  are  called  Arguments ; 
these  form  the  transition  from  Logic,  as  a Science,  to 
T * ' m Art,  is  more  properly 


It  is,  of  course,  with 


4 


INTRODUCTION. 


Logic  as  a Science,  tliat  we  have  chiefly  to  do  in  this 
volume. 

11.  The  purpose  which  we  have  now  before  us  does 
not  lead  us  to  regard  Logic  as  a means  of  discovery, 

or  of  so  constructing  such  methods  of  argu- 

good Ve4s'omn 18  mentation,  as  are  used  in  speeches  and  books, 
eoo  reasoning.  ag  £0  pe  most  successful  in  a dialectic  point 

of  view  ; not,  in  short,  to  teach  directly  liow  to  reason 
well , but  rather  what  is  good  reasoning,  and  why  it 
is  so. 

12.  In  this  view,  Logic  sustains  about  the  same 
relation  to  public  writing  and  speaking  that  Grammar 

Logic  annio-  does,  or  that  Moral  Science  sustains  to  good 
mT  ic.^Ta  morals  ; the  Science  of  Music  to  good  sing- 
science.  ing  • or  anatomy  and  physiology  to  the  prin- 
ciples of  health  and  the  practice  of  Medicine  and 
Surgery.* 

13.  As  in  Grammar,  for  example,  we  need  some 
terms  and  names,  by  which  to  represent  the  parts  of 

speech,  and  the  rules  determining  the  inflec- 
instrument  o"  tion  and  relation  of  each  part  to  others,  and 
to  the  whole  sentence  ; so  in  Logic  we  need 
names  for  each  part  of  a process  of  thought,  and 
rules  and  laws  determining  their  relation,  both  for 
the  purpose  of  discussing  and  analyzing  the  thoughts 
of  others,  and  to  assist  in  the  due  expression  of  our 
own.  Without  such  aids  it  is  impossible  to  study 
Rhetoric  and  Oratory,  or  Psychology  and  Metaphy- 
sics with  much  success ; and  they  are  of  the  greatest 
importance  in  all  departments  of  study  and  instruc- 
tion, 

14.  There  is  obviously  a distinction  between  a pro- 
cess of  thought  and  the  matter  about  which  the  thoughts 
Form  and  Mat-  are  occupied;  the  order,  arrangement,  and 
ter  of  thinking,  dependence  of  the  thoughts  upon  one  another 

* Of  course  one  may  speak  without  knowing  Grammar,  or  sing 
without  a knowledge  of  the  scientific  principles  of  harmony  and  mel- 
ody. But  he  could  speak  and  sing  much  better  with  such  knowledge, 
and  he  could  hardly  teach  or  compose  without  it. 


INTRODUCTION. 


5 


may  remain  the  same,  and  the  matter  be  different ; and 
vice  versa,  the  matter  may  remain  the  same,  and  the 
order  and  sequence  of  the  thoughts  he  different.  Hence 
the  distinction  between  the  Form  of  an  argument, 
or  processes  of  thought,  and  the  Matter  / the  Form 
denotes  merely  the  order,  dependence,  and  arrange- 
ment of  the  thoughts.  Thus,  if  I say,  “ men  are 
mortal,  and  therefore  they  should  prepare  for  death  ; ” 
and  “ men  should  prepare  for  death  because  they 
are  mortal ; ” the  Matter  would  be  the  same  in  each 
case,  but  the  form  would  be  different.  But  if  I 
should  say,  “ men  are  mortal,  therefore  they  should 
prepare  for  death  ; ” and  “ spring  is  coming,  therefore 
we  should  prepare  for  summer;”  the  Form  would  be 
the  same  in  both  instances,  but  they  would  differ  in 
matter. 

15.  But  again,  in  any  continuous  process  of  argu- 
mentation, as  in  a Speech,  an  Essay,  or  a Method. 
Book,  these  Forms  or  Formulae  may  be  combined  and 
used  in  different  relations,  and  follow  each  other  in 
different  order.  Hence,  besides  the  Matter  and  Form 
of  an  argument,  we  have  to  consider  also  the  Method  ; 
that  is,  the  way  in  which  the  Forms  are  used.  Thus, 
if  I wish  to  prove  that  four  times  twenty-five  is  one 
hundred,  I may  do  it  by  writing  twenty-five  four 
times,  each  directly  under  the  other,  and  then  add 
them  up ; or,  by  writing  it  once  with  a four  under 
it,  and  then  multiply,  the  result  will  be  the  same  in 
each  case,  but  the  Method  will  be  different  ; the 
former  is  the  Method  of  Addition,  the  latter  of  Multi- 
plication. 

16.  Logic  is  called  Formal,  and  sometimes  Ana- 
lytic, when  it  investigates  the  varieties  and  Formal  Logic, 
laws  of  the  Formulae.  When  it  goes  farther  and  in- 
quires into  the  grounds  of  the  validity  of  these  Formulae, 
it  is  called  Rational  / and  when  it  goes  one  Rational, 
step  farther,  and  takes  into  consideration  the  diversities 
of  the  various  kinds  of  matter,  and  the  peculiarities  in 
the  forms  of  expression  by  which  that  matter  is  repre- 


6 


INTRODUCTION. 


sented,  and  the  application  of  Formulae  as  modified 
Applied.  by  the  matter,  it  becomes  what  we  call  Ap- 
plied Logic. 

17.  Logic  always  presupposes,  or  takes  for  granted, 
Logic  pre-  certain  premises  or  starting-points  ; the 

truths?63  some  truth  or  falsehood  of  which  it  belongs  to 
other  branches  of  science  to  determine.  It  is  concerned 
how  far  con-  with  the  truth  of  Propositi ons,  only  so  far  as 

oMtopo*  they  are  given  as  resulting  from  certain 
sitions.  others.  But  the  first  elements  of  reasoning, 
the  primary  facts,  it  takes  from  other  branches  of  know- 
ledge, as  they  have  been  ascertained  and  established 
in  those  branches  representing  them.  It  does  not  un- 
dertake to  prove  the  self-evident  axioms  or  the  primary 
facts  of  science  in  any  department ; but  with  those 
axioms  and  facts,  given  in  philosophy  and  experience, 
it  directs  and  guides  the  mind  at  every  step,  to  its  most 
remote  results,  to  the  highest  generalizations,  and  to 
the  most  comprehensive  truths  ; as  well  as  in  every 
application  of  those  truths  to  the  practical  purposes 
of  life. 

Logic  therefore  does  not  supersede,  but  rather  pre- 
supposes, a knowledge  (derived  from  other  sources) 
of  the  subject  matter  with  which  our  minds 
laws  and  pro-  may  be  occupied.  It  simply  explains  the 
laws  by  which  the  mind  is  guided  in  arrang- 
ing and  combining  that  matter  into  scientific  systems, 
and  in  its  application  to  the  various  purposes  and  uses 
of  life. 

18.  ISTor,  again,  does  Logic  propose  a new  way  for 
doing  what  we  have  been  accustomed  to  do  in  an- 
other. From  the  earliest  development  of 

new  way  of  rea^  intellect,  and  the  very  commencement  of 
intellectual  activity,  the  mind  has  been  ac- 
customed to  think  and  to  draw  inferences,  or  think 
deductively  ; so  that  we  have  all  been  long  in  the 
practice  of  Logic,  before  we  begin  the  study  of  its 
science. 

19.  Those  forms  and  processes  in  which  we  proceed 


INTRODUCTION. 


7 


from  one  thought  to  another,  which  depends  upon  the 
preceding,  are  called  in  the  popular  language  Argu 
ments.  How  long  soever  or  how  complicated  soevei 
they  may  he,  Formula;  and  Method  are  thus  undistin- 
guished from  each  other.  The  Formulae,  or  syllogisms 
separate  processes,  each  of  which  has  one  subject  and 
but  one,  are  called  in  Logical  language,  Syllogisms  ; 
the  word  is  of  Greek  origin,  and  signifies  a putting 
together  for  the  sake  of  a Conclusion. 

20.  A Syllogism,  therefore,  first  presents  itself  to 
our  reflective  thought  as  a completed  thing  ; The  parts  of 
having  already  all  of  its  parts,  and  most  of  aSrUogism- 
them  in  their  legitimate  places,  and  connected  with  the 
other  parts.  Each  argument  consists  of  several  Pro- 
positions ; one  of  which  we  call  a Conclu-  The  parts  of 
sion,  and  the  others  the  Premises ; these  a Pr°p°sition- 
Propositions  consist  most  of  them  of  two  terms  and  a • 
Copula.  One  term,  called  the  Subject , de-  Subject-pre- 
notes  that  about  which  we  are  speaking ; dicate- 

the  other,  called  the  Predicate , denotes  what  we  say 
of  it ; and  the  Copula  is  the  verb  affirming  or  deny- 
ing the  agreement  between  the  Subject  and  Predicate : 
as  A is  B,  or  A is  not  B.  Here  “ A ” is  the 
Subject,  “ P ” is  the  Predicate,  and  “ is  ” fimS'  and 
and  “ is  not  ” the  Copula ; the  former  of  Negatlve- 
which  is  called  the  Affirmative  and  the  latter  the  Nega- 
tive Copula. 

21.  That  act  of  the  mind  by  which  the  Copula  is 
affirmed  or  denied,  is  called  a Judgment , A Jud{rment. 
or  when  expressed  in  words,  a Proposition,  ^fonsorcog- 
“ A ” and  “ B ” are  called  Terms,  and  that  nitions- 

in  the  mind  which  they  represent,  is  called  a Cognition , 
or  a Conception. 

We  come  therefore  to  Conceptions  or  Cognitions , as 
the  simplest  element  with  which  Logic,  in 
our  use  of  the  word  is  concerned,  and  the  the  starting- 
point  of  departure  with  which  we  must  polnt' 
commence  in  the  methodical  construction  of  the 
Science. 


8 


INTRODUCTION. 


22.  Logic,  however,  presupposes  some  knowledge 
of  Psychology,  and  we  must  look  to  that  for  the  expla- 
nation of  some  of  the  tacts  and  terms  which 
posef" ^syciio-  it  assumes  as  already  known.  These,  how- 
ever, for  the  sake  of  completeness,  we  will 
run  over  in  a very  cursory  manner. 


PART  I. 

ANALYSIS  OF  FORMULA. 


CHAPTER  I. 

OF  TEEMS. 

23.  Teems  are  the  words  or  signs  by  which  any 
conception  or  cognition  is  expressed,  for  the  Terms  defined, 
purpose  of  conveying  it  from  one  mind  to  another. 

SECTION  I. 

Of  Conceptions. 

24.  When  we  look  at  any  object  an  act  of  the  mind 
ensues,  which  in  psychology  is  called  per-  perceptions. 
ceiving — and  the  result  of  that  act  is  called  a Peecep- 
tion.  But  the  mind  retains  the  result  of  that  act 
after  the  object  has  been  removed  from  any  phy- 
sical connection  with  us,  and  the  mind  can  recall  it  at 
pleasure.  In  this  view  of  it,  that  result  is  called  a 

CONCEPTION  01’  a COGNITION. 

25.  Perception  is  an  instantaneous  act,  and  on 
each  occasion,  when  the  same  object  is  pre-  An  instanta. 
sented  anew  to  the  senses,  we  perceive  it  neous  act 
anew,  and  form  anew,  or  again,  a cognition  of  it.  We 
have  thus  at  the  second  time  a new  or  second  per- 

1* 


10 


LOGIC. PART  I. 


[CHAP. 


ception,  which  the  mind  compares  with  the  first,  and 
gives  the  judgment  of  identity  in  regard  to  the  object 
which  occasioned  them. 

26.  But  if  the  perceptions  differ  so  much  or  in  such 
ways  as  to  imply  a difference  in  any  of  the  insepa- 

, rable  properties  of  the  object  perceived. 

Identity  and  , • i 1 • ,1  -i  • , r t ’ 

diversity  of  ob-  the  mind  conceives  the  obiects  as  diverse 

jects  perceived.  « i i ° 

from  each  other. 

27.  In  Logic  we  regard  the  different  cognitions  of 
the  same  object  as  one  and  the  same  cognition,  ex- 

Different  co»  cePt  w^ien  we  wish  t°  take  into  considera- 
nitiinfcof  The  tion  the  changes  which  the  object  itself 

same  object.  t 10  i n , t ° 

may  undergo,  by  a change  01  those  separable 
accidents  and  modes  of  existence,  which  may  be 
changed  without  changing  the  identity  of  the  object 
itself. 

28.  A distinction  is  sometimes  made  in  the  use 
of  the  words  “ cognition  ” and  “ conception ,”  by  which 

Distinction  be-  the  former  is  used  to  denote  the  idea  of 
tionenandcocgon-  one  individual  object  only:  as  “ a man,” 
ception.  u a • anci  conception,  the  idea  of 

a class  : as  “ mankind ,”  “ villages ,”  “ pens”  &c.  I 
shall  not  take  pains  to  adhere  to  this  distinction  very 
closely  ; although  I shall  never  employ  the  word 
“ cognition  ” to  denote  the  idea  of  a class.  I shall, 
however,  very  often  use  the  word  “ conception  ” when 
I mean  to  refer  to  the  idea  or  cognition  of  an  individual 
thing  only. 

29.  A conception  or  a cognition  may  be  adequate  or 
inadequate.  It  is  adequate  only  when  it  includes,  so 

that  we  may  be  said  to  know,  all  the  pro- 
adeq2?tceeplland  perties,  uses,  purposes,  and  the  history  of  the 
inadequate.  0pject ; otherwise  it  is,  strictly  speaking,  in- 
adequate. 

30.  No  one  of  the  senses  by  itself  and  alone  can 
ever  enable  us  to  form  an  adequate  conception  of  any 

Diverse  sen-  object.  We  see  its  color;  we  smell  its  odor  ; 
fifte°to  anreaqdDi-  we  taste  its  flavor ; we  feel  its  density  and 
quale  concep-  smoothness,  &c.  Nor  can  we  ever  know, 


OF  TERMS. SECT.  I. 


11 


I-] 

or  form  an  adequate  conception,  of  any  considerable 
proportion  of  the  objects  with  which  human  knowledge 
is  occupied,  by  any  contact  of  those  objects  with  our 
own  senses.  Hence  we  have  to  rely  upon  the  testimony 
of  others,  historians,  travellers,  and  observers  in  every 
department  of  science,  for  by  far  the  largest  part  of 
what  we  know. 

31.  Moreover,  there  are  many  objects  of  thought 
of  which  we  have  conceptions,  which  how-  conceptions 
ever  never  have  and  never  can  have  any  of  ldeaa- 
connection  with  the  external  senses,  as  means  of  cog- 
nition ; such  as  truth,  justice,  virtue,  eternity,  &c. 
These  objects  of  thought  are  sometimes  called  Ideas, 
and  are  said  to  be  furnished  by  the  Reason  itself. 

32.  It  would  appear  that  man  can  have  but  very 
few,  if  any,  conceptions  or  cognitions  that 

are  strictly  and  absolutely  adequate ; and  tions  absolutely 
hence  we  are  accustomed  to  call  those  “ in-  a e<lu 
adequate  ” only,  which  are  not  sufficient  for  the  purpose 
for  which  the  conception  itself  is  used.  Thus,  if  one 
were  writing  a treatise  upon  iron,  and  did  not  know, 
or  have  as  a part  of  his  conception  of  iron,  its  property 
of  becoming  magnetized,  his  conception  would  be  in- 
adequate. But  if  his  object  was  merely  to  describe  its 
adaptedness  to  some  particular  purpose,  not  at  all 
affected  by  its  magnetic  properties,  his  conception 
might  be  adequate  for  that  purpose  ; without  includ- 
ing a knowledge  of  its  susceptibility  to  magnetic  in- 
fluences. 

33.  Logic  requires,  and  always  presupposes,  that  all 
conceptions  which  are  introduced  as  elements 

of  its  Formulae,  are  adequate  in  this  second-  how°maeJe “de- 
ary and  limited  sense.  And  if  any  concep-  qudte' 
tion  is  not  adequate,  it  must  be  rendered  so  by  further 
acquaintance  with  the  object  of  thought  which  it  repre- 
sents to  the  mind,  and  the  conception  can  be  conveyed 
adequately  to  the  minds  of  others  by  means  of  defini- 
tions, description,  &c. 

31.  The  objects  of  which  our  cognitions  are  formed, 


12 


LOGIC. PART  I. 


[chap. 


are  distinguished  as  possible,  impossible , and  real.  An 
objects  of  object  is  said  to  be  real  when  it  has  an  ac- 
w ™impo&]  tual  existence.  It  is  said  to  be  possible  when 
and  red.  jt  is  not  known  to  have  any  existence,  but  is 
nevertheless  supposed  to  have  the  possibility  of  exist- 
ing ; thus  all  realities  were  merely  possible  before  they 
were  brought  into  actual  existence.  But  an  object  of 
thought  which  can  never  exist,  is  called  impossible,  as 
a triangle  with  only  two  sides. 

35.  Realities,  or  things  real,  have  also  been  distin- 
guished into  tAvo  classes : the  Realities  of  Being  and 

„ . , the  Realities  of  Truth.  Mind,  and  all  the 

Being  and  of  forms  of  material  existence,  are  considered 
as  Realities  of  Being  or  Existence.  But, 
besides  justice,  virtue,  &c.,  which  exist  only  as  proper- 
ties of  some  intelligent  being ; there  are  also  certain 
objects  of  thought,  as  time,  space,  the  point,  the  line, 
&c.,  and  the  first  axioms  of  all  knowledge,  as  the 
whole  is  equal  to  the  sum  of  its  parts,  &c.,  which 
have  no  substantial  existence,  and  from  their  very 
nature  they  can  have  none.  Nor  yet  are  they  con- 
sidered as  merely  the  properties  of  any  substance, 
whether  material  or  immaterial.  Their  reality  would 
remain  unchanged  even  if  there  Avere  no  mind  in 
existence  to  comprehend  them.  They  are  called  Reali- 
ties of  Truth. 

36.  It  has  sometimes  been  said,  that  we  can  have 
no  conception  of  the  impossible.  But  we  must  make 

a distinction  between  a conception  and  the 
of  thefmposaf  construction  of  an  image  of  the  object  in  the 
mind.  An  image  of  the  impossible  we  can- 
not have,  but  a conception  Ave  may  have  ; for  we  use 
the  word  conception  to  denote  any  thing  of  which  we 
can  speak.  If,  therefore,  we  can  speak  of  that  which 
is  impossible,  we  can  have  a conception  of  it,  which 
comprehends  all  the  properties  that  can  be  predi- 
cated of  it — a conception  therefore  adequate  to  all 
the  purposes  for  which  a conception  can  be  needed  or 
used. 


i-3 


OF  TEEMS. — SECT.  H. 


13 


37.  The  objects  of  thought,  of  which  we  form  com 
ceptions  or  cognitions,  are  considered  as  sus-  Relations  of 
taining  several  different  relations  to  each  ConcePtions- 
other,  upon  which  deduction  depends  in  several  ways  ; 
such  as  Substance  and  Property,  Whole  and  its  Parts, 
Cause  and  Effect,  Identity,  Difference,  Resemblance  or 
Similarity,  Contrariety  and  Analogy. 

SECTION  II. 

Of  Substance  and  Properties. 

38.  By  Substance,  we  mean,  that  which  can  be  con- 
ceived of  as  existing  by  itself  {quod  substat  substance. 
per  se).  By  a Pkopekty,  an  object  of  thought  which 
cannot  be  conceived  to  exist,  except  as  in-  property, 
hering  in  some  Substance  ; thus  iron  is  a substance  ; 
hardness  is  a property  of  it. 

39.  Each  Substance  must  have  several  properties, 
and  may  have  many.  Consequently,  any 

J i J J 7.n  *'  Each  substance 

subject  may  nave  many  predicates;  thus,  has  several  pro- 
“ Matter  is  extended,”  “ Matter  is  divisi-  perties' 
ble, ” “ Matter  is  inert,”  &c.  ; — “ Iron  is  hard,” 
“ Iron  is  malleable,  ” “ Iron  is  ductile,  ” “ Iron  is 
useful,”  &c.  &c. 

40.  Each  predicate  also  may  he  predicated  of  more 

than  one  subject;  thus,  not  only  is  “Iron  Each  proper- 
hard,”  hut  “ Lead  is  hard,”  “ Diamond  is  £ “vhaies°ub® 
hard,”  “ Oak  is  hard,”  &c.  stances. 

41.  When  a term  is  thus  used  as  a predicate,  it  is 
said  to  b z predicated  of  its  subject ; and  the  predicated, 
subject  is  said  to  be  in  the  category  denoted  by  the 
predicate ; thus,  “ man  is  mortal.”  Here  category. 
“ mortal  ” or  “ mortality  ” is  said  to  he  predicated  of 
“ man,”  and  “ man  ” is  said  to  be  in  the  category 
“ mortal.” 

42.  Words  or  terms  which  may  thus  be  predicated 
of  several  subjects,  are  called  Predicables  or  PrediCabies. 
Categorematic  j those  which  cannot  be  pre-  categorematic 
dicated  of  more  than  one  subject  are  called  madticAcategore‘ 


LOGIC. — PART  I. 


14 


[chap. 


Acategorernatic.  Such  are  all  words  standing  for  indi- 
vidual objects,  proper  names,  &c. 

43.  Any  word  which  expresses  an  object,  or  the 
property  as  belonging  to  or  inhering  in  its  substance, 

is  called  a concrete,  term  : as  “ white  ” 
concrete  terms.  u iong’’  &c>  But  a worc[  that  expresses  the 

property  considered  by  itself  as  an  object  of  thought, 
Abstract  terms,  is  called  an  abstract  term;  as  “ whiteness” 
“ length”  &c. 

44.  But  such  terms  as  “ white,”  “ long,”  &c.,  while 
they  denote  the  abstract  property,  also  imply  some- 
thing that  is  “white,”  “lonq,”  &c.  Hence 

Denotatives  -1°.  t 

and  connota-  sucli  terms  are  called  (Jonnotatiyes,  and  are 
said  to  denote  the  property  of  “ length”  for 
instance,  and  to  connote  the  body  or  substance  that  is 
long. 

45.  Every  conception  is  considered  as  having  two 
sphere  and  elements,  a Sphere  and  Matter  ; or,  as  it 

ception.  is  sometimes  designated,  a Comprehension 
and  an  Intension. 

46.  The  Sphere  or  Comprehension  is  the  number  of 
sphere,  individuals  included  in  the  conception  for  which 
a word  stands.  Thus,  take  the  word  “ hard,”  or  “ hard- 
ness,” the  sphere  of  the  conception  includes  every  ob- 
ject of  which  we  can  say  “it  it  is  hard.” 

47.  The  Matter  or  Intension  of  a conception  is  the 
Matter,  number  of  properties  which  may  be  ascribed  to 
the  subject  or  substance  of  which  we  have  a concep- 
tion. Thus  with  the  subject  “Iron,”  the  matter  of  the 
conception  is  “ hardness”  “ ductility”  “ malleability” 
&c.,  including  whatever  may  be  predicated  of  iron. 

48.  Or  to  take  the  conception  “man,”  the  sphere 
includes  Csesar,  Cicero,  Washington,  &c.,&c.,  every  indi- 
vidual of  whom  we  can  say  that  “he  is  [or  was]  a 
man ; ” the  matter  of  the  conception  is  “ bimanous” 
“ biped”  “ rational”  “ religious”  “ accountable”  &c., 
including  every  thing  that  can  be  predicated  of  man, 
whether  as  a physical,  or  an  intellectual,  or  a moral 
being. 


I-] 


OF  TEEMS. SECT.  II. 


15 


49.  A distinction  is  sometimes  made  in  speaking  ol 
conceptions  between  being  contained  in  a contained  in 
conception  and  being  contained  under  it.  “ddercoJtacond 
The  Matter  is  said  to  be  contained  in  the  con-  ception- 
ception ; thus  rational  is  contained  in  the  conception 
“man.”  But  Caesar,  Washington,  Bonaparte,  Frank- 
lin, &c.,  are  said  to  be  contained  under  the  conception 
“ man.” 

50.  The  Matter  of  a conception  limits  and  deter- 
mines the  sphere ; thus  we  include  in  the  The  Matter  n- 
conception  or  class  “man,”  every  individual  mits ‘he  sphere, 
who  has  the  properties  of  a mat. 

51.  Conceptions  of  the  same  object  formed  from  dif- 
ferent points  of  view,  are  called  Alternate  Alternate  con- 
Conceptions.  Hence  Alternate  Conceptions  ceptions- 
each  denote  the  same  sphere  by  different  matter,  and 
constitute  different  names  for  the  same  object.  Thus 
“ height  ” and  “ depth  ” are  Alternate  Conceptions  of 
distance,  perpendicular  to  the  horizon,  viewed  from 
different  points.  Almost  every  object  in  Nature  has 
several  names,  according  as  it  is  viewed  in  one  or  an- 
other of  the  relations  which  it  sustains.  Thus  a Natu- 
ralist would  speak  of  certain  animals  as  “ sheep  ” 
simply  ; the  Farmer,  with  reference  to  his  farm,  would 
call  them  “ stock  /”  and  the  Commissary,  with  refer- 

T ence  to  their  use  as  a supply  for  the  army,  would  call 
them  “ provisions .” 

52.  The  cognition  of  the  sphere  and  the  matter  of  a 
conception  are  not  usually  simultaneous  acts. 

In  the  first  perception  of  a single  obiect,  we  acquired  before 
get  the  sphere  of  its  conception,  by  means 
of  some  of  its  most  obvious  properties  ; we  acquire  the 
others,  one  after  another.  In  the  question,  “ what  is 
that  f ” “ that  ” refers  to  the  sphere  of  the  conception 
which  we  already  have  in  our  minds  ; and  “ what  ” to 
the  matter  which  we  have  not  and  wish  to  acquire. 
The  same  thing  occurs  in  efforts  at  recollection.  We 
remember  that  something  happened,  was  said  or  done, 
without  remembering  what  it  was  ; we  have  the  sphere 


LOGIC. — PART  I. 


16 


[chap. 


of  its  conception  in  our  memory,  but  tlie  matter  has  for 
the  most  part  escaped  us. 

53.  The  questions  “ who  ” and  “ what,”  are  an- 
swered by  the  matter  of  a conception,  which  enables 
Questions  who?  us  to  determine  the  sphere.  But  the  ques- 
what?  and  which?  ti0n  “which,”  is  answered  by  the  sphere 
of  the  conception, — which  enables  us  to  study  out  the 
matter  for  ourselves. 

54:.  But  in  regard  to  the  conception  of  a class,  we 
get  the  matter  of  the  conception  before  the  sphere, 
since  it  is  the  matter  which  determines  and  limits  the 
sphere. 

55.  Among  the  properties  or  attributes  of  an  object 
of  thought,  we  distinguish  some  that  are  inseparable 
from  it,  as  extension  and  divisibility  from  matter  ; and 
in  a man  his  complexion,  his  features,  his  stature,  &c. ; 
and  other  properties  which  are  separable  or  different, 
at  different  times  and  in  different  places,  as  sickness 
and  health ; his  posture,  as  sitting,  standing,  or  walk- 
ing, &c.  Properties  of  the  former  kind  are  said  to  con- 

Essence  and  stitute  the  Essence * of  an  object  of  thought ; 
Modes.  the  latter  its  modes  of  existence  ; thus  the 
name  of  any  object  always  implies  all  the  essence 
of  its  reality.  But  if  we  wish  to  express  its  modes 
we  must  add  something  to  the  name,  expressive  of  that 
mode;  thus  “George  Washington”  denotes  the  man,  * 
but  does  not  imply  any  thing  of  his  modes,  as  sick- 
ness or  health,  eating  or  sleeping,  commanding  an 
army,  presiding  in  his  cabinet,  or  delivering  his  fare- 
well address. 

56.  Most  terms,  however,  denote  a substance  as 
existing  in  some  particular  mode ; and  substance  and 


* We  use  the  word  “ Essence ” in  its  Logical  sense  and  not  its  Onto- 
logical, as  denoting  that  which  it  is  in  itself,  aside  from  all  the  changes 
it  may  undergo,  without  becoming  a different  object;  and  not  that 
which  is  necessary  to  its  existence  as  an  object  in  reality.  Without 
its  Essence,  in  its  ontological  sense,  an  object  could  not  exist  at  all ; 
but  in  the  Logical  sense  it  might  exist  as  an  individual  in  another 
genus. 


I.]  OF  TEEMS. SECT.  H.  17 

mode,  in  Logic,  is  somewhat  an  arbitrary  inJ|™bfu5ice 
distinction.  Strictly  speaking,  in  the  onto-  ,namode- 
logical  sense  there  are  bnt  two  substances,  matter 
and  spirit ; and  most  other  words  denote  one  or  the 
other  of  these  substances  existing  in  some  particular 
mode ; thus  take  the  word  “ air”  it  denotes  matter 
existing  in  a certain  mode.  Again,  considering  “ air  ” 
to  be  a substance,  and  “ wind  ” is  a modal  term, 
denoting  the  existence  of  “ air  ” in  a particular  state  ; 
or  if  we  take  “ wind  ” for  one  substantive  word,  then 
“ gale  ” will  be  a modal  denoting  the  existence  of  wind 
in  some  one  of  its  modes. 

57.  When  any  property,  or  a number  of  them,  are 
considered  as  constituting  several  objects  of  thought, 
to  which  they  belong,  a class,  these  properties  are 
called  Essentia  ; thus  “ man  ” denotes  a Essentia, 
class  ; and  those  properties,  without  which  one  would 
not  be  called  a man,  are  the  Essentia  of  the  class  ; and 
the  class,  with  reference  to  these  Essentia,  Genus, 
is  called  a Genus.  Essentia  is  the  matter  of  the  con- 
ception, and  the  Genus  is  its  sphere.* 

58.  A word  denoting  a Genus  is  called  a General 
term.  But  if  the  word  denote  a number  of  General  and  coi- 
individuals,  not  by  essential  marks  belong-  lective  Terms- 
ing  to  each  of  the  individuals  separately,  but  rather 
by  some  mark  which  belongs  to  them  only  as  a whole, 
or  a body,  the  word  is  called  a Collective  term ; as 
“ congress,”  “ church,”  “ army.” 

59.  From  the  nature  of  a general  term,  whatever 
may  be  predicated  of  the  term,  may  be  pre-  Difference  in 
dicated  of  any  individual  object  included  cates.  predl" 
under  it ; thus  if  we  say,  “ man  is  a two-footed  being,” 


* I do  not  think  so  much  has  been  made  of  the  distinction  between 
the  terms  which  denote  the  matter,  and  those  which  denote  the  spheres 
of  conceptions,  as  might  with  profit,  in  explaining  what  has  been  called 
the  Predicables.  Of  these,  Porphyry,  and  after  him  the  Scholastics  gener- 
ally, have  reckoned  five:  Genus,  Species,  Differentia,  Property  and 
Accident ; the  two  first,  Genus  and  Species,  denote  spheres,  and  the 
other  three  matter  of  conceptions. 


18 


LOGIC. — PART  I. 


[CHAP. 


we  may  say  of  eacli  man,  “ lie  lias  two  feet.”  But 
this  is  not  true  of  the  collective  term  ; thus  we  can 
say  of  the  church,  “it  is  a divine  institution,”  but 
we  cannot  say  of  its  members,  “ they  are  a divine  in- 
stitution.” 

60.  Some  words  are  used  only  as  collective  terms,  as 
those  just  mentioned  ; while  others  are  sometimes  used 

some  words  as  co^ective,  and  at  other  times  as  general, 
used  in  "bom  Thus  if  we  say,  “ the  Romans  conquered 
Carthage,”  we  cannot  say  that  “ Cicero  con- 
quered Carthage,”  although  he  was  a Roman.  “ Ro- 
mans ” is  here  used  as  a collective  term.  But  if  we 
say,  the  Romans  spoke  the  Latin  language,  we  may 
say  of  Cicero,  he  spoke  the  Latin,  for  we  then  use 
“ Romans  ” as  a general  term. 

61.  When  we  consider  any  o'f  the  properties  of 
an  object  as  distinguishing  it  from  a class  to  which  it 
Differentia.  does  not  belong,  those  properties  are  called 
Differentia,  or  distinguishing  marks.  And  all  the 
individuals  which  have  these  marks  or  properties, 
species.  are  called  a Species.  Thus  woolly  hair, 
black  skin,  &c.,  if  considered  as  distinguishing  those 
who  have  them  from  other  men,  are  the  Differentia ; 
and  “ ISTegro  ” is  the  term  denoting  the  species  thus 
distinguished. 

62.  Hence  the  same  property  may  be  either  Essentia 
or  Differentia,  just  according  to  the  point  of  view  from 

Essentia  and  which  it  is  regarded.  If  we  regard  black 
SMli,  to  skin,  woolly  hair,  &c.,  as  constituting  a class, 
each  other.  then  ]^egro  js  ^ Genus,  and  these  properties 
are  Essentia.  But  if  we  have  in  mind  at  the  same  time 
“ man,”  as  a higher  and  more  comprehensive  class, 
including  those  who  have  black  skins,  woolly  hair,  &c., 
as  well  as  others  which  have  them  not,  “ man  ” is  the 
genus,  and  “ ISTegro  ” is  the  species. 

63.  Hence  those  properties  which  are  the  Differen- 
tia of  a class,  considered  as  a species,  become  Essentia 
when  the  same  class  is  regarded  as  a genus,  including 
species  under  it,  and  vice  versa. 


I-] 


OF  TEEMS. SECT.  H. 


19 


61.  Properties,  when  regarded  as  Essentia  or  Dif- 
ferentia, are  considered  Essential ; but  when  Pl.0perties  e?- 
not  so  regarded,  are  usually  spoken  of  as  jeennt'u. or  Acci' 
Accidental .* 

65.  When  any  property  is  considered  as  distin- 

guishing one  individual  from  another,  it  has  inseparable 
been  called  Inseparable  Accident,  Indivi-  Accident- 
dual  Mark  or  Peculiarity  ; and  the  object  thus  de- 
noted, is  called  an  Individual,  f individual. 

66.  Hence  Individuals  are  included  under  Species, 
SDecies  under  Genera,  and  so  on : Genus  individuals, 


hending  sphere,  and  Species  and  Individuals,  each  in 
order,  lower  and  comprehended  spheres. 

67.  Spheres  are  said  to  coincide  or  be  coincident , 
when  they  contain  some  individuals  common  spheres  coin- 
to  both ; as  for  instance,  “ Christian  ” and  poslte. dnd  0p 
“ man ; ” since  all  who  are  included  in  the  sphere 


* Properties  that  belong  to  an  individual,  or  to  the  individuals  of  a 
class  only,  are  said  to  be  peculiar  to  that  individual  or  class.  If  a pro- 
perty belongs  to  all  the  individuals  of  the  class,  it  is  general  in  respect 
to  the  class,  or  universal.  If  it  belongs  to  several  classes,  it  is  said  to 
he  common  ; a common  property. 

Properties,  when  considered  in  reference  to  some  end  or  object, 
for  which  the  thing  to  which  they  belong  is  designed  or  desired, 
are  also  called  Qualities,  or  that  which  qualifies  a thing  for  its  use  or 
end. 

f It  will  appear  from  the  above,  that  of  the  five  Predicables  of  Por- 
phyry, two,  Genus  and  Species,  must  be  nouns,  as  denoting  classes  ; 
and  the  other  three,  Differentia,  Property,  and  Accident,  will  be  adjec- 
tives ; thus,  of  John  Smith,  we  predicate,  as  they  say,  Genus , “ man 
Species,  “Caucasian;”  Differentia,  “white;”  Property,  “civilized;” 
Accident,  “ very  short,”  or  “ sitting  in  a chair.” 

Genus  and  Species  are  said  to  predicate  “in  Quid;”  Differentia, 
“in  Qualequid Property  and  Accident,  “in  Quale.” 

“Genus,”  says  Aldrich,  “is  that  which  is  predicated  of  many,  as 
their  material  or  common  part,  as  “ animal.” — Differentia,  that  which 
is  their  formal  part,  as  “rational.” — Property,  that  which  is  joined 
with  the  essence,  as  “ risible ; ” — and  Accident,  that  which  is  con- 
tingently joined  to  the  essence,  as  “white,”  “black,”  “to  sit.”  But 
in  this  account  of  terms,  he  regards  Essentia  and  Differentia  as  one,  or 
the  Differentia  as  the  Essentia  (see  Aldrich,  Oxford  ed.  1849,  p.  20,  and 
the  notes). 


20 


LOGIC. — PART  I. 


[CHAP. 


denoted  by  “ Christian,”  are  in  the  sphere  “ man  ” also ; 
since  “ Christians  are  men.” 

68.  But  if  two  spheres  have  no  individual  com- 
mon to  both,  they  are  called  contrary  or  opposite 
spheres  ; as  “ dog  ” and  “ man,”  “ Christian  ” and 
“ Mahometan.” 

Contrary  or  opposite  spheres,  however,  although 
they  may  have  no  individual  contained  under  them  com- 
mon to  both,  may,  nevertheless,  have  matter  contained 
Analogous  i11  them  in  common.  Thus  any  two  species 
spheres.  comprehended  under  the  same  genus,  must 
be  contrary  spheres ; as  black  or  white,  as  properties 
of  men,  so  that  no  object  can  be  in  both  at  the  same 
time  ; yet  black  and  white  may  be  both  species  of  men, 
in  which  the  essentia  of  humanity  is  common  to  all  the 
individuals  in  both  species.  Such  spheres  are  called 
Analogous. 

69.  That  genus  which  can  never  be  comprehended 
under  a higher  genus,  is  called  the  summum 
or  maximum  genus.  That  species  which 

can  never  comprehend  one  below  it,  is  called  the 
infima  sPe-  infana  species.  All  others  are  called  sub- 
cies-  alternate  species  and  genera.  The  genus, 

however,  which  is  next  above  any  two  or  more  co- 
ordinate species  is  called,  in  reference  to 


Summum 

Genus. 


those  species,  the  proximate  genus  y as 


Proximate 
Genus. 

“man”  is  the  proximate  genus  to  “Negro”  and 
“ Mongol.” 

70.  Those  properties  which  indicate  only  the  dif- 
separabie  ferent  modes  of  the  same  individual,  are 

Accidents.  called  Sepaeable  Accidents  ; as  sickness  or 
health  in  man,  sharp  or  dull  in  a knife. 

71.  When  attributes  are  common  to  all  the  indivi- 
duals of  two  or  more  species,  they  are  called  Indif- 
indifferentia.  ferentia,  or  points  of  indifference  y or  even 
sometimes  “ common  properties,”  as  to  have  hoofs  is 
common  to  the  horse,  the  ox,  the  goat,  the  sheep,  &c. 
Hence  the  having  hoofs  is  the  point  of  indifference  to 
those  several  species,  and  may  become  the  Essentia  of  a 


I.] 


OF  TEEMS. SECT.  m. 


21 


proximate  genus,  under  which  all  hoofed  animals  shall 
be  comprehended. 

72.  Hence  the  Differentia  is  essential  to  the  species, 
and  the  peculiarities  or  inseparable  accidents  are  essen- 
tial to  the  individual. 

73.  The  matter  of  a term,  used  as  a general  term, 
is  the  Essentia  of  the  Genus ; the  matter  The  Matter  of 
of  a term,  used  as  a specific  term,  or  to  General  Terms- 
denote  a species,  is  the  Essentia  of  the  Proximate  Ge- 
nus (and  of  course,  therefore,  of  all  higher  of  Specifio 
and  comprehending  genera),  plus  the  Differ-  Terms- 
entia  of  that  species.  And  the  matter  of  an  individual 
term  is  the  Essentia,  plus  the  Differentia,  of  individual 
plus  the  Inseparable  Accidents  or  individual  Terms- 
properties. 

71.  Besides  this  matter,  however,  every  class  must 
have  some  properties  which  are  not  considered  as  either 
Essentia  or  Differentia,  and  each  individual 
must  have  some  separable  accidents,  which  Matter  of 
are  not  necessarily  included  in  the  concep-  erms 
tion  of  the  individual.  Thus,  in  forming  a conception 
of  a man,  it  is  not  necessary  that  we  should  include  in 
the  conception  any  particular  posture,  style  of  dress, 
state  of  health,  &c.,  although  he  cannot  exist  except  in 
some  posture,  state  of  health,  &c. 


SECTION  III 

, Of  the  Whole  and  its  Parts. 

75.  The  sphere  of  any  conception  is  regarded  as  a 
whole.  But  there  are  three  ways  of  consid-  Whoies,  of 
ering  wholes  ; that  is,  there  may  be  three  threekinds- 
alternate  conceptions  of  the  same  whole,  which  we  call 
logical , Continuous , and  Collective  wholes.  The  esti- 
mate of  a whole  is  called  Quantity  ; the  process  of 
resolving  the  whole  into  parts,  is  called  Division. 


22 


LOGIC. — PART  I. 


[CHAP. 


1.  Of  Quantity. 

76.  As  there  are  three  alternate  conceptions  of  any 
whole,  so  there  ai’e  three  ways  of  estimating  the  amount 

Quantity,  of  of  that  whole,  or  three  kinds  of  Quantity ; 
three  kinds.  Logical,  Continuous , and  Discrete. 

77.  Logical  Quantity  is  that  which  estimates  the 

comparative  size  of  the  sphere  of  conceptions,  as  mea- 
Logicai  Quan-  sured  by  the  individuals  included  under 
ti,y-  them ; thus  a species  is  always  less  than  its 

proximate  genus,  and  so  on. 

78.  In  Continuous  Quantity  the  object  of  thought 
is  always  considered  simply  as  a reality  ; thus  a point, 

continuous  a line,  a surface,  a triangle,  a circle,  &c.,  are 
Quantity.  considered  as  continuous  quantity.  Theo- 
rems which  are  demonstrated  concerning  them  in  Geo- 
metry and  Trigonometry,  have  no  connection  with  the 
length  of  the  lines,  or  the  amount  of  the  area  that  may 
be  inclosed  by  them. 

79.  So  also  the  properties  which  may  be  predicated 
of  substances  in  different  degrees  of  intensity,  are  con- 
sidered as  continuous  quantity. 

80.  Discrete  Quantity  contemplates  a whole  as  a 

union  or  accumulation  of  parts.  These  parts  may  be 
Discrete  Quan-  unequal,  and  each  have  a differentia  of  its 
tity-  own.  Or  they  may  be  equal  and  have  no 

distinguishing  marks.  In  that  case  they  are  merely 
units,  and  quantity  is  mere  number ; — the  science  of 
this  kind  of  quantity  is  Arithmetic. 

81.  In  Continuous  Quantity,  the  whole  is  not  con- 
Continuous  ceived  as  made  up  of  parts,  or  divisible  into 

wholes  not  made  , ,1  -i  x •,  ■%  j 

up  of  pans.  parts  ; though  ot  course  it  may  be  so  made 
up,  and  consequently  divisible. 

82.  In  Discrete  Quantity  we  have  such  terms  as  the 
cardinal  numbers,  fractional  expressions.  Nothing,  or 

Terms  and  zero,  denotes  not  any  quantity,  but  the  ab- 
crete  hiantity!  sence  of  quantity  or  quantification  ; and  the 
last  expression,  in  discrete  quantity,  is  the  indefinite ; 


I.] 


OF  TEEMS. SECT.  III. 


23 


a sum  so  large  that  it  cannot  he  expressed,  the  limit 
cannot  he  pointed  out,  but  not  so  large  that  it  may 
not  be  increased  by  addition  and  diminished  by  sub- 
traction. 

83.  In  Continuous  Quantity  we  have  such  terms  as 
denote  indivisible  objects  of  thought ; any 

i « . • n . J -i  ° i • J Limits  m Con- 

ODjeCt  in  fact  whose  conception  does  not  lm-  tinuous  Quan- 
ply  a union  of  parts.  And  besides  names  iy‘ 
denoting  such  objects  of  thought,  we  have  also  the 
positive,  the  comparative,  and  the  superlative  forms  of 
adjectives  denoting  degrees  of  intensity;  and  the  last 
expression  of  continuous  quantity  is  “ infinite ,”  and  it 
implies  that  of  which  extension  cannot  be  predicated.* 

84:.  Logical  Quantity  begins  with  the  individual, 
and  takes  note  of  the  higher  classifications,  Limits  in  Lo- 
up to  its  last  term,  the  Absolute , — that  which  gical  Quantity- 
includes  all  being,  which  is  genus  without  ever  being 
species,  the  summum  genus. 

85.  Discrete  Quantity  is  applied  to  the  objects 
which  are  included  in  the  terms  of  the  other  Appiicatj0n  0f 
kinds  of  quantity  ; thus  a line,  or  angle,  are  JjiycrteoteLoguicai 
continuous  quantities.  But  when  we  say  the  and  continuous, 
line  has  so  many  feet,  or  the  angle  is  of  so  many  de- 
grees, we  apply  discrete  quantity  to  the  measurement 


* Even  space  and  time  form  no  exceptions  to  this  remark  : for  nei- 
ther time  nor  space,  strictly  speaking,  are  extended.  We  have  simply 
a conception  of  extension,  as  applied  to  something  in  space  or  in  time, 
but  not  to  space  and  time  themselves. 

Among  the  many  classifications  of  properties,  we  have  one  that  is 
useful  for  many  purposes — into  primary  and  secondary  ; of  which  the 
primary  can  be  predicated  of  substances  only, — the  secondary  not  of 
substances  at  all,  but  only  of  their  primary  properties ; thus,  extension 
is  a primary  property  of  matter,  length  is  a secondary  property — a 
property  of  the  extension  of  a body.  When  we  say  a body  is  so  long, 
we  mean  that  its  extension  or  extent  is  so  long.  “ Thinking  ” is  a pri- 
mary property  of  mind;  “intense,”  “close,”  &c.,  are  properties  of 
“ thinking.” 

Now,  “ infinite  ” and  “ extension,”  are  incompatible  properties  ; 
both  primary  ; and  can  neither  of  them  be  predicated  of  the  other,  nor 
in  fact  of  the  same  substances.  We  say  space  is  infinite,  and  we  have 
extension  in  space.  We  say  GOD  is  infinite,  but  we  never  speak  of 
His  extension. 


24 


LOGIC. — PART  I. 


[chap. 


of  objects  of  continuous  quantity.  In  like  manner,  when 
we  attempt  to  number  the  individuals  comprehended 
in  the  sphere  of  any  logical  whole,  whether  species  or 
genus,  it  must  be  done  in  terms  of  discrete  quantity ; 
thus  the  discrete  quantity  of  the  sphere  “ man  ” is 
800,000,000  ; that  is  the  whole  number  of  men  on  the 
earth. 

86.  But  by  far  the  greatest  part  of  the  properties 
of  substances,  considered  as  continuous  quantity,  can- 
Not  aii  objects  not  he  measured  by  discrete  quantity  ; thus 
Quantity  carfbe  we  cannot  measure  in  any  such  way  the  in- 
so  measured,  tensity  of  color,  of  taste,  of  smell,  of  density, 
&c.,  among  the  properties  of  material  substances  ; nor 
that  of  virtue,  wisdom,  courage,  &c.,  among  the  pro- 
perties or  attributes  of  mind.  We  may  be  able  to 
distinguish  a greater  or  a less  intensity — that  is,  a 
more  and  a less  — but  how  much  greater  or  less  is 
what  we  have  no  means  of  measuring  or  express- 
ing. 


2.  Of  Division. 

87.  That  process  by  which  a Whole  is  resolved  into 
its  Parts  is  called  Division  ; and,  as  there  are  three 

Division  of  kinds  of  Quantity,  so  there  are  three  kinds 
three  kinds.  0f  Division : Physical , Mathematical  or  Nu- 
merical, and  Logical. 

88.  Physical  Division  divides  continuous  quantity ; 
thus  we  divide  a loaf  of  bread  into  pieces.  Now  these 
physical.  parts  are  bread — that  is,  have  the  essentia  of 
the  whole,  but  they  have  no  proper  differentia  of  their 
own  constituting  them  different  species  of  bread — as 
“ wlieaten  bread,”  “ barley  bread,”  &c.,  but  they  are 
considered  still  as  parts,  and  are  conceived  of  in  rela- 
tion to  the  whole. 

89.  Numerical  Division  divides  a discrete  quantity 
or  number  into  parts,  each  of  which  is  considered  as 
Numerical.  a unit  or  factor  in  reference  to  that  whole. 
Thus  we  divide  a foot  into  twelve  inches,  a yard  into 


I.] 


OF  TERMS. SECT.  HI. 


25 


three  feet,  &c.,  and  the  collective  whole  with  Dividend, 
reference  to  Mathematical  Division  is  called  Dividend. 

90.  Logical  Division  divides  the  sphere  of  the 

Genus  or  Logical  Whole  into  species,  each  Logical, 
having  the  Essentia  of  the  whole  and  a Differentia 
of  its  own,  belonging  to  each  individual  contained 
under  it ; and  into  individuals,  each  having  individual 
marks  or  inseparable  accidents  of  its  own.  Logical 
Division  is  called  Classification.  classification. 

91.  Thus  physically  we  should  divide  a man  into  ^ 
head,  trunk,  and  extremities — or  into  hones,  illustration  of 
muscles,  tendons,  membranes,  fluids,  &c.  Division- 
Mathematically  we  should  divide  the  race  into  com- 
panies of  tens,  or  fifties,  or  thousands,  as  the  case  might 
be.  Logically  we  should  divide  them  into  Mongol, 
Caucasian,  and  Negroes  ; or  into  Pagans,  Mahometans, 
Jews,  and  Christians  ; or  into  civilized,  barbarous,  and 
savage,  &c. 

92.  The  number  of  individuals  included  in  any  con- 
ception or  logical  whole  may  be  divided  in 

several  different  ways.  Thus  the  inhabit-  sions  of  the 
ants  of  the  Earth  may  be  divided  ethically  same  kmd' 
into  Caucasians,  Mongols,  Negroes  ; or  politically  into 
English,  French,  Spanish,  Russians,  Chinese,  &c.  ; or 
in  reference  to  their  religion  into  Christians,  Jews, 
Mahometans,  Buddhists,  &c. 

93.  That  which  determines  us  to  any  one  of  these 
several  divisions  of  which  any  logical  whole  Divieive  Prin. 
is  susceptible,  is  called  the  Divisive  Prin-  ciple- 
ciple  or  the  Principle  of  Division.  As  in  the  example 
just  given,  Race,  Polity,  and  Religion  are  the  Divisive 
Principles  by  means  of  which  the  divisions  are  effected. 

In  mathematical  division  the  divisive  principle  is  called 
the  Divisor. 

91.  The  divisions  of  the  same  whole  effected  by 
the  different  Principles  are  called  the  Co-  coordinate  Di- 

ta*  • • A visions. 

ORDINATE  Divisions. 

95.  The  several  parts  into  which  any  whole  may 
be'  divided  by  means  o£tlie  same  Principle  of  division 

2 


26 


LOGIC. — PAKT  I. 


[chap. 


are  called  Coordinate  parts,  and  tlie  terms  denoting 
coordinate  them  are  Coordinate  terms,  as  Christians, 
pans.  Jews,  and  Mahometans,  &c. 

96.  The  Coordinate  parts  of  a numerical  Division 
Factors,  species,  are  called  Factors — with  reference  to  the 
divided  whole,  or  Dividend.  In  Logical  Division,  the 
Whole  is  called  a Genus,  and  the  Coordinate  parts  are 
Species. 

97.  But  the  parts  of  two  coordinate  divisions  of  the 
Disparate  parts,  same  whole  are  called  Disparate  parts  ; and 
the  terms  denoting  them  Disparate  terms  in  reference 
to  each  other — as  Caucasians,  Russians,  and  Maho- 
metans. 

98.  Any  one  of  these  parts  however  may  be  as- 
sumed as  a whole,  and  divided  as  though  it  were  not 
parts  assumed  included  in  a higher  and  more  comprelien- 
as  wholes.  give  w}10iCj  and  so  on,  until  the  sphere  of  the 
conception  comes  to  be  an  individual. 

99.  But  when  any  whole  is  divided  into  coordinate 
parts,  and  these  coordinate  parts  are  again  subdivided, 

subordinate  these  divisions  with  reference  to  the  first 
Divisions.  division  are  called  Subordinate,  and  the 
parts  of  these  subordinate  divisions  are  called  Subor- 
dinate parts. 

Thus  let  X be  divided  by  coordinate  divisions,  and 
illustrations,  on  different  principles  of  division,  as  follows : 

1st.  2d.  3d. 

X into  X into  X into 

A,  B and  C,  D,  E and  F,  G,  H and  I, 

X iet  X2d-  X3d-  are  coordinate  divisions. 

A,  B and  C are  coordinate  parts  in  relation  to  each 
other,  so  also  are  D,  E and  F,  and  likewise  G,  H and  I. 
But  A,  D and  G,  or  B and  F,  or  E and  G,  &c.,  are 
disparate  to  each  other. 

Let  now  A,  B and  C be  subdivided, 

A into  B into  and  C into 

a , 1),  and  c,  d,  e,f , g , h,  i. 

These  are  subordinate  divisions. 


I.]  OF  TEEMS. SECT.  m.  27 

a,  b,  c,  d,  e,f,  g,  h and  i are  all  subordinate  parts 
to  X18t- 

But  a , b and  c,  &c.,  are  coordinate  to  each  other, 
and  d , g , &c.,  are  disparate  to  each  other,  as  in  the 
first  division  the  parts  occupying  similar  places  were 
disparate. 

100.  Any  conception  including  in  its  sphere  more 
than  one  individual,  though  it  may  denote 

but  a coordinate  or  a subordinate  part  in  uo^mayTea 
reference  to  another  and  more  comprehen-  " )U  e' 
sive  whole,  may  become  nevertheless  a logical  whole 
or  unity  itself  with  coordinates  and  subordinates  under 
it.  And  each  term  or  conception,  whether  whole,  co- 
ordinate or  subordinate,  and  in  whatever  degree  of 
subordination,  until  we  come  to  a term  that  denotes 
but  one  individual,  will  have  a sphere  and  a matter  of 
its  own,  and  so  be  capable  of  a logical  division. 

101.  As  we  have  said,  the  parts  in  any  Logical 
Division  are  called  Species.  And  besides  the  Alternate  parte 
Coordinate,  Disparate,  and  Subordinate  Spe-  orSPecies- 
cies  just  described,  we  have  in  Logical  Division  Alter- 
nate Species  also.  These  are  species  the  Differentia 
of  which  is  a part  of  the  matter  of  Alternate  concep- 
tions of  the  same  object.  Thus  statesman  and  philoso- 
pher may  be  Alternate  conceptions  of  the  same  indivi- 
duals, so  that  the  same  men  may  be  both  statesmen  and 
philosophers,  though  of  course  an  individual  may  be 
one  without  being  the  other.  In  this  view  of  the  mat- 
ter statesmen  and  philosophers  are  said  to  be  Alternate 
Species. 

102.  The  last  element  of  a Logical  Division  is  called 
individual.  But  the  individual  may  be  either  Absolute  m- 
Absolute  or  Relative.  It  is  absolute  when  it  dividuals- 
can  be  divided  no  farther.  Thus  the  mind  is  an  abso- 
lute individual ; the  chemical  simples  such  as  iron, 
sulphur,  sodium,  &c.,  are  also  absohite  individuals, 
because  they  cannot  be  resolved  or  analyzed  into  any 
component  elements. 

103.  On  the  other  hand,  most  of  the  objects  of 


28 


LOGIC. PART  I. 


[chap. 

thought  are  merely  relative  or  assumed  individuals  ; 

Relative  in-  that  is,  they  are  individual  only  in  reference 
dividuais.  to  the  purposes  for  which  they  are  at  the 
time  before  the  mind.  In  this  view  “ man  ” is  an 
individual,  in  reference  to  any  classification  of  the 
animal  kingdom.  But  in  reference  to  a classification 
of  substances  as  spiritual  and  material,  man  is  not  an 
individual — his  mind  belongs  to  one  class  and  his  body 
to  another.  So  with  reference  to  a Treatise  on  Materia 
Medica,  carbonate  of  soda,  for  instance,  is  an  indi- 
vidual ; but  in  reference  to  chemical  analysis  it  is  a 
compound,  resolvable  into  carbonic  acid  and  sodium. 

104:.  The  following  are  regarded  as  the  fundamental 
vf8rns  of  Di‘  Canons  of  Division. 

(1.)  The  coordinate  parts  must  contain  all  that  was 
contained  in  the  whole,  and  nothing  that  was  not  con- 
tained in  it. 

(2.)  Each  coordinate  part  must  have  a narrower 
sphere  or  be  smaller  than  the  divided  whole. 

(3.)  ISTo  unit  or  individual  can  be  contained  in  more 
than  one  coordinate  part. 

Thus  if  one  should  divide  his  library  into  the  co- 
Exampies.  ordinate  division,  folios,  quartos,  octavos,  &c., 
and  Greek,  Latin,  English,  French,  German,  &c.,  and  into 
philosophy,  history,  physics,  mathematics,  poetry,  &c., 
each  division  would  be  good.  But  if  he  should  divide 
into  folios,  octavos,  Greek,  history,  philosophy,  &c.,  the 
division  would  be  faulty.  It  would  not  be  made  on 
any  one  principle  of  division,  and  the  same  book  might 
be  included  in  several  of  the  parts. 

105.  The  division  of  a Logical  Whole  into  Alternate 
Species  is  only  an  imperfect  division,  and  does  not 
fulfil  the  conditions  as  above  specified.  It 
desernatvioi£te  results  from  the  very  nature  of  Alternate 
tiiL-se  canons.  conceptiong>  that  they  may  be  all  of  them 

predicated  of  the  same  object ; since  they  are  but 
Alternate  conceptions  or  different  views  of  that  object. 
Hence  if  they  are  taken  as  the  Differentia  of  Species, 
the  same  individual  may  be  in  more  than  one  of  them 


I.] 


OF  TEEMS. SECT.  IV. 


29 


at  once  ; thus  a man  may  he  a Christian,  a gentleman, 
and  a scholar,  all  at  the  same  time.  Still,  ^ contain 
however,  the  Alternate  Species  must  include  Aye  Xvidl 
all  the  individuals  comprehended  under  the 
Logical  Whole  or  Proximate  Genus.  If  we  divide  the 
writers  of  a nation,  for  instance,  into  poets  and  prose 
writers,  the  same  writer  may  belong  to  both  species ; 
but  there  must  he  no  one  who  does  not  belong  to  one  or 
the  other  of  them. 

SECTION  IY. 

The  relation  of  Cause  and  Effect. 

106.  When  any  object  of  thought  is  considered  in 
relation  to  that  which  brought  it  into  exist-  Cause  and 
ence,  or  as  having  had  a beginning,  it  is  Effect- 
conceived  of  as  an  Effect  ; and  when  an  object  is  con- 
ceived in  reference  to  what  it  may  bring  into  existence, 
it  is  conceived  of  as  a Cause. 

107.  Nearly  every  object  of  thought  is  conceived 
as  both  Cause  and  Effect ; — Effect  in  refer-  Every  object 
ence  to  something  which  has  preceded  it  as  a the“asedcause 
condition  of  its  existence  ; and  as  Cause  in  or  Effect- 
reference  to  something  which  follows  it  or  whose  exist- 
ence is  either  occasioned  or  conditioned  by  it. 

108.  Thus  starting  from  any  object  of  thought  con- 
ceived as  effect,  we  may  direct  our  thoughts  Cauge  Abso. 
to  its  cause,  and  from  that  cause  conceived  ‘ute- 

as  effect,  to  its  cause,  and  so  on  until  we  come  to  the 
First  Cause  or  Cause  Absolute.  So  it  is  that  whatever 
we  know  by  its  own  properties  directly  we  always 
know  and  conceive  of  as  effect ; and  the  mind  of  neces- 
sity refers  to  something  else  as  the  ground  and  cause 
of  its  being.  But  when  we  come  at  last  to  that  Being 
whom  no  man  hath  seen  or  can  see,  and  whom  we 
know  only  through  the  manifestation  of  His  wisdom, 
and  power,  and  goodness — through  the  effects  of  these 
transcendent  attributes,  Him  we  know  only  as  Cause. 
He  is  not  only  the  Cause  and  Creator  of  all  things 


30 


LOGIC. PART  I. 


[CHAP. 


visible  and  invisible,  but  He  is  also  the  Cause  as  Au- 
thor of  the  Revelation  which  He  has  made.  Hence  we 
know  Him  only  through  His  works  and  His  Word, 
and  the  mind  refuses  to  conceive  of  Him  as  an  Etfect. 

109.  But  with  this  only  Exception,  cause  and  etfect 
cause  and  Ef.  are  but  alternate  conceptions  of  the  same  ob- 

Conceptions.ate  ject  of  thought.  Each  object  of  thought  is 
susceptible  of  both  conceptions,  and  each  in  turn  de- 
mands both.  In  this  view  all  objects  of  thought,  con- 
sidered as  causes,  are  distinguished  into  Absolute,  and 
Relative — the  One  only  being  Absolute,  all  others 
being  relative. 

110.  Again  we  conceive  of  Mind  as  a cause  in  a 
different  sense  from  what  matter  can  be.  Motion,  in 
cause  primary  matter,  always  refers  the  mind  to  something 
and  secondary.  0U£  0f  tdig  moving  mass,  as  its  cause — this 
cause  we  call  a Force.  But  if  we  see  a being  possess- 
ing mind,  in  motion,  we  are  content  to  consider  him- 
self as  the  cause  of  his  own  motion ; and  reason  is 
satisfied  when  we  refer  to  his  will  as  the  cause  of  the 
movement..  Hence  we  distinguish  between  Primary 
and  Second  causes,  and  call  those  Primary  which  are 
sufficient  causes — and  those  Secondary  which  only  refer 
us  to  something  else  as  the  cause  of  its  acting,  as  cause ; 
and  so  on  until  we  come  to  intelligent  moral  Agency, 
as  the  only  Primary  Causes. 

111.  Besides  the  above  distinctions  there  are  seve- 
ral other  senses'in  which  the  word  Cause  is  used,  or  in 
which  the  object  of  one  conception  may  be  regarded 
as  the  cause  of  the  object  of  another. 

(1.)  The  Efficient  Cause  is  that  from  which  emanates 
Efficient  cause,  the  force  that  produces  the  Effect. 

(2.)  The  Occasional  or  Exciting  Cause  is  that  which 
occasional.  puts  the  Efficient  Cause  in  operation,  as  the 
spark  in  the  explosion  of  gunpowder. 

(3.)  The  Material  Cause  is  the  matter  or  Essentia 
Material.  of  which  any  thing  consists.* 


* As  the  Essentia  of  any  class  considered  as  a Genus  is  the  Material 
of  that  Genus,  the  Essentia  may  be  called  with  reference  to  this  fact 
the  Material  Properties. 


OF  TERMS. — SECT.  IV. 


31 


<1 

(4.)  The  Formal  Cause  is  that  which  determines 
the  specific  mode  of  the  existence.*  Formal. 

(5.)  The  Final  Cause  is  that  for  which  any  thing 
exists  or  is  done  ; and,  Final. 

(6.)  We  have  also  what  are  called  Negative  Causes, 
as  when  we  say  “ the  want  of  rain  caused  Negative, 
a severe  drought,” — “ the  absence  of  heat,”  or  which 
is  the  same  thing,  “ cold  congeals  the  river.” 

112.  Of  the  six  kinds  of  Cause  just  enumerated,  the 
1st  and  2d,  the  Efficient  and  Occasional,  common  Name? 
are  usually  spoken  of  as  Causes  ; and  much  ofthem- 
confusion  often  arises  from  not  distinguishing  between 
them.  The  Material  Cause  is  usually  spoken  of  not  as 
a cause  but  as  “ the  nature  of  the  thing  ; ” the  Formal 
Cause  as  its  “ characteristic  ; ” and  the  Final  Cause  as 
its  “design”  or  “object.” 

113.  Thus  if  we  take  an  act  of  virtue,  the  person 
who  performed  it  is  the  Efficient  Cause  ; illustrations, 
the  motion  which  induced  him  to  do  it  is  the  Occa- 
sional Cause ; the  fact  of  its  being  a free  act  and  not 
one  of  necessity,  or  even  instinct,  is  the  Material  Cause ; 
the  nature  of  the  act,  its  conformity  to  right  rules  of 
action  is  its  Formal  Cause  or  characteristic,  and  makes 
it  a virtue  and  not  a vice  ; and  the  object  for  which  it 
was  done  is  its  Final  Cause. 

114.  Causes  are  sometimes  considered  as  Transient , 
Permanent , or  Immanent. 

A Transient  Cause  is  one  which  passes  away  after 
its  efficiency  has  been  exerted.  Thus  occa-  Transient  cause, 
sional  causes  are  for  the  most  part  transient,  as  the 
spark  that  ignites  the  powder.  A Perma-  Permanent  cause, 
nent  Cause  is  one  that  remains,  and  from  which  the 
effect  is  continually  flowing — as  the  sun  and  the  lamp 
are  permanent  causes  of  light.  An  Imma-  immanent  cause, 
nent  Cause  is  one  that  remains  in  its  effect ; the  Mate- 
rial and  Formal  Causes  are  always  Immanent. 

* As  the  Differentia  of  Species  are  the  Formal  Cause  of  the  Species, 
■with  reference  to  this  fact  they  may  he  called  for  the  sake  of  con- 
venience the  Formal  Properties. 


32 


LOGIC. PAKT  I. 


[CHAP. 


115.  Causes  with  reference  to  the  fact  that  they 
^called  a n to j always  exist  before  the  Effect,  are  sometimes 
consequents!11  called  Antecedents  merely.  So  also  Effects 
for  the  same  reason  are  sometimes  called  Consequents 
or  Consequences  merely. 

116.  Effects  are  either  Immediate  or  Remote.  The 
^immediate  Ef-  Immediate  effect  is  that  which  follows  at 
Remote.  once ; the  Remote  effects  or  consequences 
are  those  which  appear  afterwards,  but  not  until  after 
an  interval  in  which  they  are  not  seen. 

117.  Again,  Effects  or  Consequences  are  Direct 
and  Accidental.  Direct  when  necessarily  following 

Direct.  Acci-  fi'om  the  activity  of  the  Cause,  and  always 
dental  implied  in  the  conception  of  its  agency. 
But  those  effects  which  are  not  invariable  attendants 
upon  the  activity  of  the  Cause,  and  are  not  considered 
as  necessarily  implied  in  it,  or  as  necessary  to  its  ade- 
quate conception  as  a cause,  are  called  Accidental ; 
undesigned,  and  in  reference  to  an  intelligent  cause  they 
are  called  Undesigned. 

SECTION  V. 

Of  Difference , Identity , Resemblance  and  Analogy. 

Difference  is  of  two  kinds — (1)  in  kind,  and  (2)  in 

Difference  of  rlcwvroo 
two  kinds. 

118.  Although  any  common  name  may  he  used  as 
genus,  yet  there  are  certain  obvious  and  natural  pro- 

Difference  in  perties  of  all  objects  of  cognition,  by  which 
kind-  they  are  referred  to  natural  classes.  In  this 

classification  these  more  obvious  properties  are  assumed 
as  the  basis  of  the  classification.  When  therefore  two 
objects  do  not  agree  in  possessing  each  the  same  pro- 
perty in  this  natural  classification,  they  are  said  to 
differ  in  kind. 

119.  But  when  two  objects  of  cognition  are  con- 
ceived as  belonging  to  the  same  natural  genus,  and  are 
m Degree.  compared  only  with  reference  to  some  one 
property  or  class  of  properties  which  they . have  in 


!•] 


OF  TERMS. SECT.  VI. 


33 


common,  they  are  said  to  differ  in  degree  only.  In  this 
case  the  objects  possess — the  one  more  and  the  other 
less  of — the  property  or  properties  which  are  made  the 
basis  of  the  comparison.  They  differ  only  in  the  degree 
or  intensity  in  which  they  possess  the  property  com- 
mon to  both,  and  in  reference  to  which  they  are  com 
pared. 

120.  When  the  difference  is  only  in  separable  acci- 
dents then  it  is  said  to  be  “ identity .”  It  is  identity, 
the  same  individual  under  different  circumstances  or 
at  different  times  ; thus  “ sick  ” or  “ well,”  “ sitting  ” 
or  “ walking,”  “ sleeping  ” or  “ waking,  ” with  re- 
gard to  a man  ; “ hot  ” or  “ cold,”  “ round  ” or  “ irre- 
gular,” “ bright  ” or  “ rusty,”  &c.,  of  a piece  of  metal, 
are  mere  separable  accidents  denoting  different  states 
or  modes  of  the  same  individual  substance. 

121.  The  properties  common  to  any  two  or  more 
individuals  conceived  as  belonging  to  the  same  species, 
constitute  what  is  called  Similarity  or  lie-  similarity  and 
semblance.  And  the  properties  which  are  Contranety- 
different  in  any  two  or  more  individuals  conceived  as 
belonging  to  the  same  species,  constitute  Contrariety. 

122.  Hence  similarity  and  contrariety  are  between 
individuals  conceived  as  belonging  to  the  same  species. 
Or  these  terms  may  be  applied  in  the  same  way  to 
species  conceived  as  comprehended  within  the  same 
proximate  genus. 

123.  The  properties  in  common  between  individuals 
conceived  as  belonging  to  opposite  or  differ-  Analogy, 
ent  species  constitute  what  is  called  Analogy. 

SECTION  VI. 

Of  Definition  and  Description. 

Before  proceeding  to  explain  more  fully  the  terms 
which  will  be  of  frequent  use  throughout  this  Treatise, 
it  may  be  well  to  say  what  we  mean  by  a Definition, 
and  what  by  a Description ; reserving  the  fuller  dis- 
cussion of  the  subject  to  the  chapter  on  Method. 


34r 


LOGIC. PAKT  I. 


[CHAP. 


124.  A Definition  is  any  Proposition  in  which  the 
Definition.  word  or  thing  defined  is  the  subject,  and 
the  predicate  gives  us  the  matter  of  its  conception. 

125.  A Description  is  any  Proposition  which  indi- 
Description.  cates  the  sphere  of  a conception,  either  by 
enumerating  its  parts  or  pointing  to  the  place  in  which 
or  the  time  where  it  may  be  found. 

SECTION  VII. 

Of  the  Quality  of  Terms. 

126.  The  Quality  of  a Term  indicates  the  manner 
Quality  of  Terms,  in  which  it  represents  the  conception  or 
cognition  for  which  it  stands.* 

• 

* Aristotle  divided  the  categories  into  ten  : Substance,  Quantity, 
Quality,  Relation,  Place,  Time,  Position,  Possession,  Action,  Passion, 
(Organ,  c.  iv.)  And  he  adds  (Top.  I.  c.  ix.),  “for  accident,  and  genus, 
and  property,  and  definition,  [I  am  not  responsible  for  his  divi- 
sion,] will  always  be  in  one  of  these  categories,  since  all  propositions 
through  them  signify  either  what  a thing  is,  or  its  quality,  or  quantity, 
or  some  other  category.”  Aristotle’s  illustration  is,  Substance  “ man,” 
Quantity  "one,"  Quality  “white,”  Relation  “greater,”  where  “ in  the 
Forum,"  when.  “ yesterday ,”  Position  “ sitting,”  Action  “ whatever  he 
may  be  doing,"  Passion  “ whatever  may  be  being  done  to  him" 

Now  it  is  very  possible  that  every  thing  that  can  be  said  of  any  sub- 
ject may  be  included  in  one  or  another  of  these  categories.  The  list 
seems  to  be  very  complete.  But  I have  been  unable  to  see  its  utility, 
and  therefore  I have  omitted  it.  And  in  that  respect  it  is  like  much 
else  in  the  writings  of  this  Father  of  Logical  Science. 

At  a later  period  Kant  gave  another  list  of  the  categories.  Aristotle 
had  classified  them  from  the  outward  properties  of  things.  Kant 
classified  them  from  the  ideas  determining  their  cognition — into  four, 
each  of  which  contains  under  it  three  varieties  or  dimensions. 

( One.  I Real. 

I.  Quantity  •<  Some.  II.  Quality  ■<  Limited. 

( All.  ( Non-Real. 

f Substance,  or  Property. 

III.  Relation  ■<  Cause,  or  Effect. 

( Action,  or  Reaction. 

( Possible,  or  Impossible. 

IV.  Modality  ■<  Existence,  or  Non-Existence. 

( Necessary,  or  Contingent. 

This  list  of  categories  is  important  rather  to  Metaphysics  than  to 
Logic,  as  determining  the  conditions  and  possibility  of  knowledge  rather 


I.] 


OF  TEEMS. SECT.  VII. 


35 


127.  We  have  already  had  occasion  to  ^concrete  ana 
explain  what  we  mean  by  concrete  and  ah-  De°^tjve  and 
stract  terms  (see  43),  by  denotative  and  con-  connotative™ 
notative  (see  44),  by  substantive  and  modal  MU0bdsjfntiveand 
(see  55)  terms. 

128.  A term  denoting  a class  is  called  general  with 
reference  to  its  including  more  than  one  in-  General  Terms, 
dividual,  and  specific  with  reference  to  its  specificTerms. 
distinguishing  them  from  all  others. 

We  will  now  proceed  to  notice  a few  more  of  the 
differences  in  the  Quality  of  a Term. 

129.  Terms  denoting  the  same  conception  are  called 

SynOnymOUS.  Synonymous. 

130.  Terms  denoting  Analogous  Spheres  are  called 
Analogous  Terms. 

131.  Terms  having  the  same  logical  force,  though 
not  analogous  or  synonymous,  are  called  Equipollent. 
Equipollent. 

132.  Terms  which  denote  sometimes  one  conception 
and  sometimes  another  are  called  Ambiguous.  Ambisuous. 

133.  Terms  which  cannot  be  predicated  of  the  same 
subject  at  the  same  time  and  in  the  same  respect,  are 
called  Incompatible.  Thus  “ sitting  ” and  incompatible. 
“ standing  ” cannot  be  predicated  of  the  same  man  at 
the  same  time.  “ Master ” and  u servant”  can  be  pre- 
dicated of  the  same  subject  at  the  same  time,  but  not 
in  the  same  respect.  Thus  one  may  be  the  servant  of 
his  superior  and  master  of  his  dog ; but  he  is  not  master 
and  servant  in  respect  to  the  same  thing  or  in  the  same 
respect. 

134.  A Positive  Term  is  one  which  implies  the 
reality  of  that  which  it  denotes.  All  terms  positive, 
therefore  denoting  genus,  species,  or  individuals,  or  the 
properties  of  them,  are  Positive. 

than  the  deduction  of  one  thought  from  another,  and  the  systematic 
construction  of  those  thoughts  into  knowledge  and  science. 

In  the  following  Sections,  therefore,  I have  confined  myself  to  such 
classifications  of  terms  as  seemed  to  be  useful  for  the  purposes  of  deduc- 
tion, and  omitted  all  others  on  the  ground  that  the  inclusion  of  \yhat- 
ever  is  not  useful  is  a hinderanee. 


36 


LOGIC. PART  I. 


[CHAP. 


135.  But  the  sphere  of  a positive  term  is  a limited 
pTh*  sphere  of  sphere,*  and  excludes  all  that  has  not  the 
limited?  Lrm8  Essentia  of  the  conception  denoted  by  the 
Positive  ; thus  the  conception  circle  excludes  from  its 
sphere  all  figures  that  are  not  circles. 

136.  A Positive  sphere  therefore  necessarily  im- 
plies another,  in  which  are  included  all  objects  that 

implies  a Ne-  do  not  possess  the  attributes  contained  in 
gative  sphere.  (]ie  matter  of  that  conception.  The  term 
that  denotes  this  sphere  is  called  a Negative  Term. 

137.  The  sphere  of  the  Negative  Term  is  the  com- 
Neeative  a plement  of  that  of  its  Positive  in  the  sum- 

the  positive,  mum  genus,  or  absolute  totality  ot  tilings. 

138.  A Privative  Term  is  one  which  denotes  an 
privative.  object  or  class  of  objects  in  which  there  is 
an  absence  of  some  property,  usually  considered  as 
belonging  to  the  conception  of  its  proximate  genus  or 
species. 

139.  When  we  speak  of  the  Essentia  as  that  with- 
out which  an  individual  cannot  belong  to  a genus  in 
illustrations,  natural  classification,  we  refer  rather  to  the 
conception  than  to  the  actuality  of  the  individual. 
Thus  one  would  say  that  reason  is  of  the  Essentia  of 
man,  and  yet  we  would  not  say  that  an  idiot  was  not  a 
man.  We  recognize  the  idiot  as  one  who  is  accident- 
ally deprived  of  that  which  belongs  to  the  idea  or  con- 
ception of  his  species.  He  is  no  less  a monster,  a 
lusus  natures,  than  a horse  with  reason  or  a dog  that 
could  talk. 


* This  is  so,  or  Pantheism  is  inevitable.  Infinite  is  not  so  much 
without  limits  as  out  of  limits ; as  red  is  not  so  much  a long  color 
as  a color  out  of  length  ; that  is,  not  included  in  any  Genus  of  which 
any  of  tile  terms  denoting  extension  can  be  predicated.  But  if  the 
term  Goo  does  not  denote  a limited  sphere,  then  of  course  there  is 
nothing  which  is  not  God — God  is  all — or  Pantheism.  But  it  is  one 
thing  to  say,  the  term  “God”  denotes  a limited  sphere;  and  to  say, 
that  God  is  limited,  or  not  infinite.  “Limited”  and  “infinite”  are 
not  antithetic  or  opposites  in  the  same  kind,  like  “ long"  and  “ short 
"red"  and  "yellow,"  but  disparates  rather,  like  “long"  and  “red," 
or  “ short  ” and  “ yellow." 


OF  TEEMS. SECT.  VTI. 


37 


i.] 

140.  Thus  “ idiotic  ” when  predicated  of  man,  or 
“ blind  ” when  predicated  of  an  animal,  are  Privative 
terms.  We  do  not  speak  of  “ dumb  ” as  predicable 
of  a triangle,  although  it  implies  the  presence  of  no 
property,  but  only  the  absence  of  one  which  never 
belongs  to  a triangle.  So  with  “ idiotic  ” in  reference 
to  a mountain  or  a brute  even  ; Privative  though  it  be, 
it  denotes  the  absence  of  a Differentia  or  Property 
which  can  never  be  predicated  upon  the  Essentia  of 
“ angles,”  of  “ mountains,”  or  of  “ brutes.” 

14:1.  The  Negative,  as  we  have  said,  is  the  comple- 
ment of  the  Positive  in  the  Summum  Genus  Privativescom 
or  absolute  totality  of  things.  But  the  Priva-  piem?nVofthe 
tive  is  the  complement  of  the  Positive  in  prokmate  cee 
the  Proximate  Genus  only  ; as  “ wise  ” and 
“idiotic”  in  reference  to  men — “blind”  and  “see- 
ing” in  reference  to  “animals,”  which  thus  become 
joro  hac  vice  a proximate  genus. 

142.  Hence  it  is  obvious  that  Privative  terms  are 
vastly  more  frequent  than  Negatives.  In  But  few  Ne 
fact  there  are  hut  few  really  Negative  terms  satlve  Terms- 
in  use.  Which  they  are  can  be  determined  only  by  the 
usus  loquendi  of  each  language,  and  the  peculiarities 
of  localities  and  of  the  authors  who  use  them  ; thus  A 
and  non- A are  a Positive  and  its  Negative. 

143.  The  distinction  between  them  however  is  less 
necessary  to  be  made  on  account  of  the  fol- 
lowing facts  with  regard  to  their  use.  If  the  th™pd7st1nction 
term  occurs  as  a subject,  it  is  of  no  import-  tives and  pnva- 
ance  whether  it  be  Negative  or  Privative ; tue6I.‘otsreat- 
though  not  the  same  they  are  equipollent  in  that  posi- 
tion. But  if  the  term  occur  as  a Predicate  it  is  of 
no  importance  for  the  most  part,  since  the  subject  itself 
is  the  sphere  of  the  Proximate  Genus,  and  thus  limits 
the  individuals  which  are  taken  into  the  scope  of  the 
judgment,  and  all  individuals  comprehended  in  the 
sphere  of  the  subject  and  not  included  in  any  position 
used  as  a Predicate,  must  be  included  in  its  Privative 
as  well  as  its  Negative.  Thus  let  “ wise”  be  a positive 


3S 


LOGIC. PART  I. 


[chap. 


Predicate,  and  we  say  “ some  men  are  wise,  and 
some  men  are  foolish.”  It  is  of  no  importance  whe- 
ther foolish  is  a Negative  or  a Privative  term,  since  in 
either  case  and  alike,  it  includes  all  men  who  are  not 
“ wise  ; ” since  some  men  are  “ wise  ” and  the  rest  are 
“ otherwise.” 


SECTION  Yin. 

Of  the  Quantity  of  Terms. 

144.  Terms  expressive  of  Discrete  Quantity  are 
either  Numerals  or  Ordinals.  The  Numerals  denote 

Numerals  and  the  number  of  units,  as  “ three  fi  “four” 
ordmais.  “five  ; ” and  the  Ordinals  the  order  in  which 
any  particular  unit  stands  with  reference  to  the  other 
units  in  any  given  series,  as  “ third  f “ fourth , “sixth.” 

145.  Terms  expressive  of  Discrete  Quantity  are  also 
divided  into  such  as  express  units  merely,  as  “ one,” 

units,  Tens,  “ two,”  “ three,”  &c. ; such  as  express  tens  of 
and  Hundreds.  xinits,  as  “ten,”  “ twenty  “ thirty”  &c. ; 
and  such  as  express  hundreds,  as  “ one  hundred ',” 
“ two  hundred ,”  &c.  This  classification  of  the  terms 
in  Discrete  Quantity  is  of  great  service  in  discussing 
the  elementary  Methods  of  the  science  of  Numbers. 

146.  We  have  also  other  classifications,  as  “odd” 
and  “ even,”  “ roots,”  “ squares,”  “ cubes,”  “ surds,” 

“ rationals,”  &c.  But  as  we  shall  not  go 
Roots.'  Powers!  into  the  discussion  of  the  Logic  of  Discrete 
Quantity — far  enough  to  require  the  use  of 
these'terms — it  will  be  unnecessary  to  discuss  them  at 
length. 

147.  Then  we  have  such  terms  as  “ Positive  ” and 
“ Negative fi  which  have  been  already  considered  in 

positive  and  the  preceding  sections.  As  expressions  of 
D?screte6 Guam  Discrete  Quantity  they  have  relation  to 
tity-  “ zero ” or  “ nothing”  They  indicate  the 

distance  above  and  below  that  starting  point — the  one 
showing  the  number  of  units  above  or  more  than 
nothing,  and  the  other  the  number  below  or  less. 


I.] 


OF  TEEMS. SECT.  Tin. 


39 


148.  The  word  “ infinite  ” when  used  in  discussions 
of  Discrete  Quantity,  indicates  either  the  absence  of 
Quantity  altogether,  or  that  the  object  of 
thought  is  out  of  the  sphere  of  Discrete  Discrete  than0 
Quantity  altogether.  That  which  is  infi-  t,ty' 
nitely  small  is  Nothing ; and  that  which  is  infinitely 
large  is  something  with  which  the  terms  of  Discrete 
Quantity  are  incompatible.  Thus  if  we  divide  nothing 
by  two  |,  the  answer  or  quotient  is  said  to  be  infinitely 
small ; that  is,  there  is  none.  If  we  divide  two  by 
nothing  f , the  quotient  is  said  to  be  infinitely  large  or 
infinite.  But  there  is  no  quotient  at  all.  There  is  no 
division  in  either  of  the  above  cases,  for  the  obvious 
reason  that  we  cannot  divide  without  both  a divisor  and 
something  to  be  divided.  In  each  case  therefore  we 
perform  no  operation  and  get  no  results  in  Discrete 
Quantity.  “ Small  ” and  “ large  ” imply  Continuous 
Quantity ; but  when  they  become  infinite,  they  are 
beyond  the  reach  of  Discrete  Quantity.  This  is  shown 
also  by  the  fact  that  they  never  occur  in  the  process 
of  a calculation,  but  only  are  results  at  the  close  of  the 
process. 

149.  In  Continuous  Quantity  “ Positive  ” is  a 

term  which  denotes  the  reality  of  Quantity,  Positive  and 
and  “ Negative  ” is  a term  which  denotes  continuous 

its  absence ; the  same  in  relation  to  Con-  Quantity, 

tinuous  Quantity,  as  “ Infinite  ” does  in  relation  to 
Discrete  Quantity. 

150.  Then  we  have  “ Compa/ratives  ” and  “ Super- 
latives, and  these  too  in  opposite  directions 

from  the  Positive  ; thus  let  us  take  “ wise  ” parities,’  and 

...  . j -l  ,,  Superlatives. 

as  a positive  term,  and  we  have  “ m,ore 
wise,”  and  “ less  wise,”  as  Comparatives  of  opposite  m- 
opposite  intensity ; and  “ most  wise,”  and  tensity- 
“ least  wise,”  as  Superlatives  of  opposite  intensi- 
ties. 

151.  In  Logical  Quantity  we  have  but  two  varieties 
of  terms  to  be  noticed. 

152.  Any  term  denoting  a Logical  Whole,  whether 


40 


LOGIC. — PART  I. 


[chap. 


Individual,  Species,  or  Genus,  is  called  a Distributed 
Distributed  ami  term.  And  any  term  denoting  any  unde- 
undistributed.  tei'mined  part  of  such  a whole  is  called  an 
Undistributed  term. 

153.  All  individual  terms  are  therefore  always  and 
necessarily  Distributed.  Any  term  denoting  genus  or 

species,  standing  alone  and  singly,  or  used 
out  a sign  are  as  the  subject  of  a Proposition,  is  always 
taken  as  Distributed,  or  in  its  broadest  sense, 
unless  the  contrary  is  indicated  by  some  word  or  words 
limiting  its  comprehension,  as  “ some  men,”  “ many 
books,”  “ few  wise  men.” 

154.  we  are  to  notice,  however,  that  any  words 
which  give  the  Differentia  of  an  included  species, 

specific  terms  constitute  thereby  a specific  and  not  an  un- 
are  distributed,  distributed  term.  As  in  the  cases  just  given, 
“ some  men”  does  not  indicate  what  part  or  how  many 
of  the  race  of  men  we  intend  to  speak  of.  “ Many  ” im- 
plies a larger  part  than  “ few  ” ordinarily,  but  neither 
of  them  enable  us  to  distinguish  the  individuals  in- 
tended, from  the  others  included  in  the  same  general 
term.  But  if  we  say  “ wise  men,”  “ religious  books,” 
the  adjectives  “ wise”  and  “ religious  ” give  differ- 
entia of  species,  comprehended  under  the  genera 
“ man  ” and  “ books  ; ” and  the  specific  term  “ wise 
men  ” is  as  completely  a distributed  term  as  the  generic 
“ men  ” itself — some  Avise  men  ” would  be  undis- 
tributed of  the  specific  term. 

SECTION  IX. 

Of  the  Opposition  of  Terms. 

155.  Among  the  properties  of  substances  we  per- 
ceive some  Avhicli  always  imply  others.  Thus  length  as 

opposition  of  a property  of  matter  always  implies  breadth, 
Terms.  g0  that  whatever  has  the  one  must  have  the 
other.  (A  line  can  hardly  be  said  to  have  length ; it 
rather  is  length.)  A beginning  always  implies  an  end, 
extension  always  implies  divisibility,  &c. 


OF  TEEMS. SECT.  IX. 


41 


I-] 


156.  The  relation  of  such,  properties  is  called  a 

Relative  Opposition,  and  may  be  of  two  Relative  op- 
kinds.  positio"- 

(1.)  Where  the  correlative  properties  inhere  in  the 
same  substance,  as  “ length  ” and  “ breadth,”  In  the  same 
“ beginning  ” i«nd  “ end,”  “ extension  ” and  substance- 
“ divisibility,”  &c. 

(2.)  Where  they  necessarily  imply  different  sub- 
stances, as  “ parent  ” and  “ child,”  “ sub-  rn  different 
ject”  and  “ruler;”  and  the  two  terms  substances- 
taken  together  are  called  Correlates. 

157.  Again  there  are  certain  properties  which  im 
ply  the  absence  of  certain  others  ; this  relation  consti- 
tutes Contrary  Opposition,  as  “ vice  ” and 


Contrary 

Terms. 


“ virtue,”  “ white  ” and  “ black,”  “ hot  ” 
and  “ cold.”  In  fact  the  differentia  of  coordinate  spe 
cies  are  always  contraries  to  each  other.  Contrary 
terms  are  called  Antithetic  in  relation  to  Antithetic 
each  other. 

158.  There  are  properties  also  which  may  coexist 
in  the  same  substance,  yet  in  such  a way  that  the  more 
of  the  one  the  less  of  the  other  — these  are  called 
Sub-contraries.  Thus  “ bitter  ” and  “ sweet  ” sub  -contraries, 
are  words  which  denote  two  sub-contrary  spheres,  since 
whatever  object  is  the  one  is  capable  of  being  the 
other.  The  same  object  may  be  both  at  the  same 
time,  that  is  “ bitter-sweet,”  and  the  more  of  the  one 
the  less  of  the  other.  Beauty  and  Utility  are  two 
more  such  sub-contrary  spheres,  since  the  same  object 
may  be  both  beautiful  and  useful,  and  for  the  most 
part  that  which  is  the  most  of  the  one  is  the  least  of 
the  other. 

159.  In  the  case  of  both  Correlative  and  Antithetic 
terms  the  one  always  implies  the  other,  though  in  dif- 
ferent ways,  and  in  both  cases  also  one  of  the  pair  can 
never  be  fully  understood  without  the  other. 

160.  When  terms  are  opposite,  both  in  Quality  and 
Quantity,  they  are  said  to  be  in  a Conteadic-  contradictory 
toey  Opposition.  Thus  anv  Positive  term  Terms- 


42 


LOGIC. — PART  I. 


[chap. 


and  its  undistributed  Negative  have  a Contradictory 
Opposition,  as  “ men,”  and  “ some  not-men ; ” or  “ some 
men,”  and  “ all  not-men.” 

161.  From  the  foregoing  discussions  the  following 
inferences  may  be  drawn,  which  it  will  be  useful  to 
remember.  • 

(1.)  Of  any  term  as  subject  the  specific  term  next 
above  it,  as  animal  to  man,  or  its  matter,  may  be  predi- 
cated, and  so  on  through  the  subaltern  genera  and 
species  up  to.  the  summum  genus. 

(2.)  Of  correlative  terms  : 

(a)  If  they  are  correlated  in  the  same  subject,  if 
one  is  predicated  of  a subject  the  other  must  be 
also. 

(b)  If  they  are  correlatives  in  opposition  subjects, 
the  other  cannot  be. 

(3.)  Of  sub-contraries , both  may  be  predicated  of 
the  same  subject. 

(4.)  Of  contraries , both  cannot  be  predicated  of  the 
same  subject. 

(5.)  Of  contradictories , if  one  is  not  predicable  of  a 
subject  the  other  must  be. 


nj 


OF  PKOPPSITIONS. — SECT.  I. 


43 


CHAPTER  H. 

OF  PEOPOSITIONS. 


SECTION  I. 

Of  Judgments. 

162.  A judgment  is  an  act  of  the  mind  affirming  a 
relation  between  two  objects  of  thought  by  judgments, 
means  of  their  conceptions.  Hence  in  every  judgment 
there  must  be  metaphysically  two  conceptions  and  the 
act  affirming  the  relation.  The  conceptions  are  repre- 
sented physically  by  the  terms  Subject  and  Predicate, 
and  the  act  affirming  the  relation  by  the  Copula,  and 
the  judgment  thus  expressed  is  a Proposition. 

163.  It  will  be  observed  that  this  definition  distin- 
guishes the  judgment  from  the  command,  DisilLished 
the  question,  and  the  exclamation ; inasmuch  Emamuatsionsn,s’ 
as  no  one  of  them  affirms  a relation  of  agree-  &c- 
ment  or  disagreement  between  the  terms  or  concep- 
tions which  are  included  in  them.  With  these  forms 
of  speech  Logic  has  nothing  to  do,  except  as  we  shall 
see  by  and  by  the  question  is  sometimes  to  Question  and 
be  regarded  as  furnishing  the  matter  upon  Judsment- 
which  a judgment  is  sought.  Thus  we  say  “ A is  B ; ” 
this  is  a judgment.  But  in  the  question  “is  A,  B?” 
we  furnish  the  matter  A and  B,  and  ask  for  the  copula ; 
or  iii  the  other  form  “ what  is  A?  ” we  furnish  the  sub- 
ject and  copula,  and  ask  for  the  Predicate. 

164.  The  terms  of  a Proposition  are  regarded  as 


44 


LOGIC. — PART  I. 


[CHAP. 


constituting  its  matter.  Hence  judgments  may  be  in 
the  same  matter  though  differing  in  form, 

lVTnttpr  and  O O 7 

Form  or  judg-  as  .A.  is  B,  and  B is  A ; and  A is  not  B,  or 
B is  not  A ; are  all  in  the  same  matter. 
But  A is  B,  and  A is  0,  and  B is  0,  &c.,  are  the  same 
in  form  though  differing  in  matter. 

165.  By  the  scope  of  a judgment  we  mean  its  com- 
prehensiveness in  either  continuous  or  discrete  quantity, 
scope  of  judg-  Thus  “ one  man  is  walking,”  and  “ two  men 
ments.  are  walking,”  differ  in  scope  ; the  latter 
being  twice  as  large  as  the  former.  Again,  “ men 
catch  at  straws,”  and  “ men  catch  at  straws  when  they 
are  drowning ,”  differ  in  scope  also  ; the  former  being 
more  comprehensive,  since  the  latter  limits  “ the  catch- 
ing at  straws  ” to  some  particular  time  or  condition. 

166.  Judgments  have  been  divided  into  three  classes 
species  of  bi  reference  to  the  Belation  which  they  aff 

judgments.  firm  to  exist  between  the  parts  of  the  Judg- 
ment— Categoric,  Conditional,  and  Disjunctive. 

167.  This  Division  corresponds  with  the  three  great 
fundamental  relations  of  conceptions  to  one  another — 
namely,  the  Substance  to  its  Attributes  or  Properties, 
the  Cause  and  its  Effects,  and  the  Whole  and  its  Parts, 
which  have  been  discussed  in  the  preceding  chajiter. 

168.  If  the  judgment  simply  affirms  or  denies  an 
categorical.  agreement  between  a Subject  and  a Predi- 
cate it  is  called  Categorical , as  A is  B,  or  A is  not  B. 

169.  If  the  judgment  affirms  the  reality  of  a Predi- 
conditionai.  cate  on  the  ground  of  the  reality  of  the  Sub- 
ject, the  judgment  is  called  Conditional , thus,  If  A is, 
B is. 


170.  But  if  the  judgment  affirms  the  reality  of  one 
Disjunctive.  of  two  terms,  on  the  ground  that  the  other  is 
not  real,  the  judgment  is  called  ^Disjunctive  / thus,  Either 
A or  B is.  If  A is  not  B is. 

171.  But  in  both  the  Conditional  and  the  Disjunc- 
cOnditi0nai  and  tive  the  terms  instead  of  being  single  cogni- 
?iyjumoreethTn  tions  or  conceptions  are  always  categorical 
two  terms.  judgments.  Thus  If  A is,  B is,— is  the  same 


n.] 


OF  PROPOSITIONS. SECT.  I. 


45 


as  if  A is  existing  or  is  real , B is  existing  or  real.  And 
so  with  the  Disjunctives,  Either  A or  B is  existing  or 
real. 

172.  Now  as  the  Conditional  affirms  its  Predicate 
on  condition  that  the  subject  is  real,  and  the  Hypothetical 
Disjunctive  on  the  condition  that  it  is  not  iudsmeut3- 
real ; the  two  judgments  unite  in  the  point  of  indiffer- 
ence that  they  both  affirm  under  a condition  ( sub  con- 
ditioner e’£  virodeaecad).  They  are  sometimes  considered 
as  two  species  of  Hypothetical  judgments. 

173.  But  as  the  members  of  both  the  Conditional 
and  the  Disjunctive  jugments  are,  by  them-  Presuppose  ca- 
selves  considered,  Categorical  Judgments  ; minis'*  Juds’ 
these  judgments  are  never  primary.  The  judgment 
itself,  that  is  the  subjective  act,  is  as  simple  as  in  the 
Categoric  Judgments  ; but  there  must  always  have 
been  a Categorical  Judgment  before  either  form  of  the 
Hypothetical. 

174.  We  will  therefore  postpone  the  consideration 
of  the  Conditional  and  Disjunctive,  until  after  we 
have  examined  the  Categorical  Judgments. 

175.  Categorical  Judgments  are  of  three  categoricals  of 

* . i & ® three  kinds. 

kinds  : 

(1.)  In  the  first  place  they  simply  affirm  or  deny  the 
Predicate  of  the  Subject,  as  A is  B,  or  A is  not  B ; or 

(2.)  They  compare  the  Subject  with  the  Predicate, 
as  A is  greater  than  B,  or  A is  equal  to  B. 

(3.)  They  represent  the  Subject  and  the  Predicate 
as  sustaining  some  numerical  relation  to  each  other,  as 
A is  one-half  of  B,  or  A is  three  times  as  much  as  B. 

176.  The  first  of  these  are  Categoricals  in  Logical 
Quantity,  which  we  will  call  Pure  Categori- 
cals • the  second  class  are  Categoricals  in 
Continuous  Quantity,  and  are  called  Com-  comparative. 
parative  or  Relative  Judgments  ; and  the  third  are  in 
Discrete  Quantity,  and  in  one  of  their  forms  of  expres- 
sion constitute  what  are  called  Probable 
Judgments. 

177.  We  will  therefore  consider  these  Judgments 


Pure  Catego- 
ricals. 


Probable. 


46 


LOGIC. PART  I. 


[CHAP. 


and  the  Propositions  in  which  they  are  expressed  in 
* the  following  order. — (1)  Categoricals  in  Logical  Quan- 
tity : (a)  simple,  (b)  complex,  (c)  compound. — (2)  Com- 
parative Judgments. — (3)  Probable  Judgments. — (4) 
Conditional ; — and  (5)  Disjunctive  Judgments. 

SECTION  II. 

Of  the  Terms  in  a Proposition. 

178.  Categorical  Judgments  have  been  defined  as 
those  which  affirm  or  deny  simply  an  agreement  be- 
tween the  Subject  and  Predicate. 

179.  Since  a judgment  necessarily  implies  two  cog- 

two  Terms,  nitions,  two  terms  must  be  contained  ex- 
pressly or  implicitly  in  every  Proposition.  In  some 
cases  there  is  no  difficulty  in  finding  them  at  once,  as 
“ man  is  mortal .”  But  in  other  cases  it  is  not  obvious 
to  the  inexperienced  at  first  glance  what  the  terms 
really  are.  A little  consideration  however  will  always 
bring  them  to  light.  Thus  if  we  say  “ John  loves,” 
we  have  for  subject  obviously  “John  ; ” we  predicate 
of  him  “ loving ,”  and  the  proposition  is  the  same  as 
“ John  is  loving .”  “ God  exists.” — Here  existence  is 

what  we  predicate  of  God,  and  we  may  say  “ God  is 
existing.”  It  is  the  same  if  we  say  “ there  is  a God  ; ” 
“ God  ” is  still  the  subject  though  coming  after  the 
copula,  and  “ existence  ” the  predicate  implied  in  the 
copula  itself.  Or  again  if  we  say  “ it  rains,” — “ rain  ” 
is  the  subject,  and  that  which  we  predicate  of  it  is  that 
it  is  falling,  “ rain  is  falling.” 

180.  In  English  the  subject  is  placed  before  the 

subject  placed  copula  for  the  most  part,  yet  not  always  or 
puia.  necessarily.  And  it  is  otten  necessary  to 

know  something  of  the  connection  of  a proposition  with 
others,  or  of  the  circumstances  under  which  it  was 
uttered,  in  order  to  decide  which  is  the  Subject  and 
which  the  Predicate.  But  that  is  always  Subject  *of 
which  we  are  speaking,  and  that  is  Predicate  which  is 
affirmed  of  it. 


n.] 


OF  PROPOSITIONS. SECT.  II. 


47 


181.  We  use  the  Subject  chiefly  with  reference  to 
the  sphere  of  its  conception,  and  the  Predi-  subject  used 
cate  with  reference  to  its  matter  ; that  is,  in  ?pf|hnce 
the  subject  we  are  thinking  of  the  thing  rffeerencetetoit3 
itself  in  its  substance,  and  in  the  predicate  of  maWer- 

its  properties  or  what  may  be  said  of  it. 

182.  The  Subject  may  be  either  a noun  or  a verb 
in  the  infinitive  mood,  as  “ man  is  mortal,”  what  may  tJ0 
“ to  err  is  human.”  But  for  the  most  part  Subject 
when  the  subject  is  a verb  in  the  infinitive  mood,  it  is 
placed  after  the  copula  in  English,  as  “ It  is  hard  to 
deny  oneself.”  Here  “to  deny  oneself”  is  manifestly 
the  subject,  and  that  which  is  said  of  it  is  that  “ it  is 
hard.” 

183.  The  Predicate  of  a Proposition  may  be  either 
a noun  denotative,  or  an  adjective  connota-  What  Predi. 
tive,  or  a verb  in  the  infinitive  mood  ; — as  cate- 

“ man  is  an  animal,”  “ man  is  mortal,”  “ to  be  good  is 
to  be  great.” 

184.  In  perceiving  an  object  we  perceive  it  as  a 
whole — substance  and  properties  all  com-  objects  Per- 
bined  in  one  objective  reality.  But  by  a “holes, 
subsecpent  process  of  reflection  and  analysis  we  come 
to  separate  it  in  our  thoughts  into  substance  and  pro- 
perties, and  each  of  these  properties  may  be  predicated 
of  the  object.  We  see  the  snow,  we  Analyze  it  into 
substance  and  properties,  we  think  of  whiteness  and 
say  the  snow  is  white ; because  that  property  is  one 
of  those  which  was  contained  in  our  very  perception 
of  the  snow. 

185.  Any  property  which  belongs  thus  to  a logical 

whole,  whether  it  be  individual  or  universal,  The  formation 
may  be  predicated  of  that  whole.  of  judgments. 

186.  When  a property  is  ascribed  to  a subject  in 
any  judgment,  the  subject  being  taken  as  a Propositions 

t • , • -i  T5  i , 7 , 1 • t resolvable  into 

distributed  term,  the  judgment  may  be  re-  terms, 
solved  into  a cognition,  as  “ the  snow  is  white,”  into 
“ white  snow.” 

187.  But  when  the  property  is  ascribed  to  an  un- 


48 


LOGIC. PAJJT  I. 


[chap. 


determined  part,  the  subject  being  undistributed,  we 
into  Terms  may  resolve  the  judgment  into  a term,  mak- 
w*th  Modais.  jng  the  Predicate  an  adjective,  as  “ some 
ti’ees  are  deciduous,”  becomes  “ deciduous  trees.”  By 
this  process  that  which  in  the  judgment  was  the  pro- 
perty  of  a genus,  becomes  now  the  differentia  of  the 
species  included  in  the  genus,  or  next  higher  and  com- 
prehending conception.  Thus  by  every  change  in  our 
form  of  expression,  and  by  every  assertion  we  make,  we 
change  our  classification.  We  have  all  noticed  such 
Examples.  expressions  as  “ horse-chestnut  ” and  “ chest- 
nut-horse, ” “ brandy -peach  ” and  “ peach-brandy,  ” 
“ sand  paper  ” and  “ paper  sand.”  They  illustrate  the 
point  under  consideration — they  invert  the  order  of 
classification  ; the  noun,  here  as  in  all  cases,  denoting 
the  genus,  and  the  adjective,  when  not  a mere  explica- 
tive, the  differentia  of  the  intended  species,  which  is 
really  the  subject  of  the  predication. 

188.  Logically,  therefore,  the  use  of  an  adjective 
The  Logical  before  a noun  is  indicative  of  a contained 

tives.  species,  as  in  the  cases  just  given,  “sand 

paper”  and  “paper  sand”  for  instance — the  former 
denoting  a kind  of  paper  as  distinguished  from  other 
kinds,  and  the  latter  denoting  a kind  of  sand  distin- 
guished from  other  kinds  of  sand. 

SECTION  III. 

Of  the  Copula. 

189.  The  Copula  is  the  formal  Cause  or  constitutive 
copula.  of  the  Judgment.  The  effect  of  the  Copula 
in  pure  categorical  judgments  in  Logical  Quantity,  is 
that  it  includes  the  subject  in  the  sphere  of  the  Predi- 
cate ; that  is,  supposing  the  Copula  to  be  affirmative — 
and  of  affirmative  Copulas  only  will  we  speak  at  the 
present. 

190.  Some  Categoricals  affirm  an  identity  between 
in  identical  the  Subject  and  the  Predicate.  These  are 

judgments.  called  'Identical  Judgments.  As  “Victoria 


II.] 


OF  PROPOSITIONS. SECT.  H. 


49 


is  the  Queen  of  England,”  “ common  salt  is  chloride  of 
sodium,”  “ a triangle  is  a figure  with  three  sides,”  &c. 

191.  But  in  all  other  cases  the  Copula  in  pure 
Categoricals  includes  the  Subject  within  the 

sphere  of  the  Predicate  ; and  of  course  shows  tegoricau6  the 
a coincidence  of  sphere  to  the  extent  of  the  coincideuclreof 
comprehensiveness  of  the  sphere  of  the  Sub-  andolAf  m"t- 
ject,  and  an  analogy  between  the  spheres  so 
far  at  least  as  the  matter  of  the  conception  of  the  Pre- 
dicate extends— which  is  of  course  the  Essentia  of  the 
Genus  denoted  by  the  Predicate. 

The  simplest  form  of  the  Copula  is— “ is,”  or  “ are.” 
As  “ A is  B.”  “ All  men  are,”  &c.  &c.  coFp°u™s  of  th8 

192.  But  we  sometimes  have  the  verb  “ to  be  ” in  past 
or  future  tenses.  “ Alexander  was  King  of  CoPuia  jn  iq. 
Macedon,” — “ To-morrow  will  be  Tuesday.”  transkive  Verb3- 
For  the  most  part  there  is  no  necessity  of  being  more 
precise  in  expressing  or  analyzing  the  Copula.  But  if 
there  is,  the  thing  is  easily  done.  “ Alexander  is  that 
which  was  King  of  Macedon ,” — “ To-morrow  is  that 
which  will  be  Tuesday.”  This  destroys  indeed  the 
rhetorical  beauty  or  structure  of  the  sentence.  But 
Logic  takes  no  note  of  such  things. 

193.  Again  and  more  frequently  still  the  Copula  is 
merged  in  a transitive  verb.  As  “Fortune  copun  in  van. 
favors  the  brave,”  “ Fortune  is  that  which  sitive  Verbs- 
favors  the  brave.” — “ A wise  King  makes  happy  sub- 
jects,” “ A ivise  King  is  that  which  makes  happy 
subjects.” 

191.  Mistakes  are  often  made  in  attempting  to  de- 
cide what  is  Copula  and  what  belongs  to  the  Mistakes  to  be 
terms  in  a Proposition,  Thus  if  we  say  that  avoided- 
“ heat  is  the  cause  of  fluidity,”  we  must  not  suppose 
that  “ heat  ” and  “ fluidity  ” are  the  terms,  all  the  rest 
being  copula.  The  predicate  in  this  case  is  not  “ fluid- 
ity,” but  the  cognition  expressed  by  the  words  “ the 
cause  of  fluidity.”  Again,  “ animal  includes  man.” 
Here  it  has  been  supposed  that  the  predicate  is  in- 
cluded in  the  sphere  of  the  subject.  But  the  predicate 


50 


LOGIC. — PAKT  I. 


[chap. 


is  not  “ man  ” merely,  but  “ that  which  includes 
man  ; ” that  is,  “ animal  ” is  the  genus  which  includes 
“ man.” 

195.  In  saying  that  the  effect  of  the  Copula  in  cate- 
gorical Propositions  in  Logical  Quantity,  is  to  include 

The  Real  and  the  subject  in  the  sphere  of  the  Predicate,  I 
BfectDof'sthe  do  not  mean  to  say  that  such  is  the  intended 
copula.  effect ; or  that  in  forming  the  judgment  the 
sphere  of  the  Predicate  is  at  all  before  the  mind,  or 
consciously  in  the  thoughts.  Thus  when  I say  that 
“ man  is  an  animal,”  I am  not  thinking  of  animals  / 
that  is,  I am  not  thinking  of  the  class  of  objects  to 
which  I refer  man.  On  the  contrary,  I use  the  predi- 
cate as  a general  term — with  reference  to  its  Essentia 
and  not  its  sphere  ; not  the  individuals  contained  in  it 
are  the  objects  of  thought,  but  simply  and  only  the 
necessary  matter  of  the  general  conception. 

196.  blow  this  necessary  matter  of  the  general  con- 
ception, as  we  have  seen,  is  only  the  Essentia  of  the 
predicate  used  genus  to  which  the  subject  is  referred.  It 
8?iuarofe  the  does  not  include  the  Differentia  of  any  com- 
Genus.  preheuded  species,  still  less  of  course  the 
individual  properties  Avhich  distinguish  one  individual 
from  another,  and  without  which  no  conception  of  any 
one  of  the  individuals  included  in  the  genus  can  be 
formed. 

197.  In  the  act  of  judging  the  Subject  is  distinctly 
and  conspicuously  before  the  mind  as  a sphere,  and  the 

The  subject  sphere  of  the  Predicate  is  only  indirectly 
““s‘s  jn°n the  and  remotely  before  the  mind.  Hence  it  is 
thoughts.  the  sphere  of  the  subject  and  the  matter  of 
the  predicate  between  which  the  mind  consciously  and 
intentionally  affirms  the  agreement.  The  effect,  how- 
ever, is  that  the  subject  is  of  necessity  thereby  in- 
cluded in  the  sphere  of  the  predicate  as  a proximate 
genus. 

198.  Since  the  copula  in  pure  categorical  judgments 

Pure  catego-  includes  the  subject  within  a higher  sphere, 

classification.  “ or  refers  it  to  a comprehending  class,  the 


n.]  OF  PROPOSITIONS. — sect.  m.  5] 

principles  of  classification  are  necessarily  implied  in 
the  investigation  of  categorical  Propositions. 

As  we  have  already  defined  the  principal  terms 
used  in  Classification,  we  shall  need  to  resume  the  sub- 
ject only  for  the  purpose  of  stating  its  general  princi- 
ples, so  far  as  they  are  implied  in  or  requisite  for  the 
purposes  of  Logic. 

199.  When  there  are  more  than  the  three  grades, 
Genus,  Species,  and  Individual,  the  same  prjn(,iple  ofcias- 
principle  holds  in  the  subordination  of  to'mjie'thcSfthree 
classes.  Thus  the  matter  contained  in  the  grades- 
conception  of  the  Genus  = Essentia, 

“ Species  = Ess.  + 1st  Differentia. 

1st  Sub-species  = Ess.  + 1st  Diff.  + 2d  Differentia. 

2d  Sub-species  = Ess.  + 1st  + 2d  + 3d  Differentia. 

“ Individual  = Ess.  + 1st  + 2d  + 3d  Dif.  + Pecu- 

liarities. 

200.  But  besides  this,  each  class  will  have  proper- 
ties, and  each  individual  accidents,  which  Necessaryand 
are  not  included  in  the  above  analysis  of  the 

matter  of  the  conceptions  ; what  is  named  tions- 
above  is  necessarily  included  in  the  conception.  All 
else  is  merely  contingent  and  accidental. 

201.  It  will  appear  from  the  above  statement  of 
subordinate  spheres  and  their  matter,  that  comprehensive- 
the  more  comprehensive  of  individuals  the  “teES 
les  comprehensive  of  matter  any  conception  ofMatter- 
will  be ; and  vice  versa , the  more  comprehensive  of 
matter  the  less  comprehensive  of  individuals. 

202.  As  the  principles  of  classification  are  founded 
in  the  nature  and  truth  of  things,  the  Differ- 

entia  of  a species  must  therefore  always  sus-  Differentia  to 
tain  a certain  relation  to  the  Essentia  of  any  s“entld' 
genus  under  which  it  can  be  included.  Thus  the  Dif- 
ferentia of  “ wise  ” and  “ foolish,”  of  “ pious,”  of 
“ humane,”  &c.,  can  be  predicated  only  upon  the  Es- 
sentia of  “ man,”  as  a genus.  We  can  predicate 
“right”  and  “wrong”  in  a moral  sense  only  of  the 
acts  that  proceed  from  freedom  of  choice,  and  having 


52 


LOGIC. PART  I. 


[chap. 


this  [freedom]  as  an  essentia.  We  can  predicate  “hard,” 
“soft,”  “heavy,”  “light,”  &c.,  &c.,  only  of  material 
things. 

203.  When  a word  is  used  to  denote  a class,  we  use 
it  without  the  article  in  English,  as  “ man,”  &c.  We 

words  denot-  do  not  say  that  “ an  animal  ” denotes  merely 
wfthoU^thesard-  ^Ie  essentia — that  which  is  essential  to  all 
tide.  animals.  For  when  the  word  is  thus  used 

with  the  article  it  denotes  some  existing  animal  with- 
out denoting  precisely  which  perhaps,  and  consequently 
implies  the  differentia  and  accidents  of  an  individual 
also.  But  the  word  “ animal  ” when  used  simply  and 
without  the  article,  whether  definite  or  indefinite,  im- 
plies merely  that  which  is  essential  to  the  animal 
nature,  and  by  no  means  all  that  is  found  in  any  exist- 
ing animal.  We  can  form  no  image  in  our  minds 
representing  merely  “ animal ; ” the  image  must  be 
of  an  animal — some  animal  already  existing,  or  which 
might  possibly  exist — and  consequently  the  image 
must  contain  in  it  more  than  is  represented  by  the 
generic  term. 

204.  The  words  “ the  animal  ” always  refer  to  some 
individual  animal  before  the  mind,  and  consequently 

t imply  the  individual  properties  necessary  to 
articles  “ the  ” the  conception  of  the  individual  referred  to. 
used  with  the  ^ An  animal ,”  used  as  a subject,  as  also 
subject.  « animals  ” in  the  plural,  always  implies 
something  more  than  the  mere  essentia  of  the  genus 
“animal,”  since  all  animals  and  each  animal  must  have 
some  system  of  nutrition  for  instance  ; and  the  essentia 
of  such  a system  is  always  implied  when  we  speak  of 
“ an  animal,”  or  of  “ all  animals.”  But  yet  as  all  animals 
have  not  the  same  systems,  no  one  individual  system 
can  be  included  in  the  conception.  But  when  we  use 

with  the  pre-  the  word  “an  animal  ” as  a Predicate,  the 
dicate.  matter  of  the  conception  is  precisely  the 

same  as  if  we  had  used  “ animal  ” without  the  article, 
as  “ man  is  an  animal  ” is  merely  ascribing  to  man  the 
essentia  of  animal  nature,  just  as  when  we  say  “ man 
is  animal.” 


n.] 


OF  PROPOSITIONS. SECT.  IV. 


53 


205.  We  have  thus  far  been  speaking  of  the  classi- 
fications that  are  based  upon  those  insepara- 

, • j?i-iXi'i  ,i  , Conspicuous 

Die  properties  ot  o meets  which  are  the  most  properties  not 

A “ i , • , the  only  basis 

conspicuous,  hint  such  properties  are  not  of  ciassifica- 
always  or  the  only  ground  of  classifications. 

In  classifications,  for  the  purposes  of  the  Natural 
Sciences,  a very  different  principle  is  often  found  the 
most  conducive  to  the  end  in  view. 

206.  The  classifications  of  the  Natural  Sciences  or 

Natural  Genera  or  Species,  are  for  the  most  ^ 

part  based  on  properties  which  are  not  only  turafciassifid- 
inseparable,  hut  also  incapable  of  different 
degrees  of  intensity — of  a more  and  a less — thus  “ man 
is  biped.”  We  have  no  such  expressions  as  “more 
biped,”  “ less  biped,”  &c.  So  it  is  also  with  such 
words  as  “ quadruped,”  “ winged,”  “ dogtoothed,” 
“ hoofed,  ” — and  the  words  “ mental,”  “ material,” 
“ eternal,”  “ infinite,”  &c.  They  have  no  comparatives. 
It  is  the  same  with  the  mathematical  differentia,  “ tri- 
angular,” “ quadrilateral,”  “ circular,”  “ elliptical,” 
“ conical,”  &c. 

207.  But  besides  this  it  is  obvious  that  any  mode 
or  separable  accident  whatever,  may  be  the  L0gicai  ciassi- 
ground  or  principle  of  a mere  transient  fication3- 
classification.  Thus  we  may  classify  the  inhabitants 
of  a city  into  sick  and  well — those  in  a room  as  those 
that  are  sitting,  and  those  that  are  standing,  &c.  The 
mode  or  accident  which  serves  as  differentia  to  these 
transient  classifications  must,  however,  be  such  that 
the  terms  denoting  its  presence  and  absence  cannot  be 
both  predicated  of  any  one  individual  at  the  same  mo- 
ment of  time  and  in  the  same  respect. 

208.  It  will  follow  from  what  has  been  said,  that  if 
any  individual  contains  the  Differentia  of  individuals 
any  species,  it  must  be  included  in  that  spe-  cieudeTmysp2- 
cies  ; and  if  either  individual  or  species  con-  cies- 
tains  the  Essentia  of  any  genus,  it  must  be  contained 
in  that  genus.  The  Differentia  are  essential  to  the 
species,  and  the  Peculiarities  to  the  individual.  The 


LOGIC. — PAKT  I. 


54 


[chap. 


peculiarities  also  are  tlie  differentia  of  the  indivi- 
dual. 

209.  Hence  every  assertion  we  make  by  the  neces- 
sary laws  of  thought  or  of  affirmation,  makes  a classifi- 
cation. It  refers  the  subject  to  a class  whose 

classify  their  essentia  or  dinerentia,  as  we  may  regard  the 
•class,  a genus,  or  a species,  is  denoted  by  the 
predicate.  We  say  that  “this  man  is  a farmer;”  we 
refer  him  to  the  class  of  farmers.  We  say  “the  snow 
is  falling  we  refer  it  to  a class  of  things  whose  dif- 
ferentia or  essentia  is  denoted  by  the  state  expressed 
by  the  predicate  “ falling.”  We  say  “ God  is  good  ;” 
we  refer  Him  to  the  class  of  objects  which  are  charac- 
terized by  the  attribute  or  property  of  goodness.  We 
say  “ the  wicked  will  be  punished  ; ” we  refer  them  to 
a class,  whose  only  point  or  property  in  common  it 
may  be,  is  the  doom  that  is  declared  by  the  predi- 
cate to  await  them  ; and  yet  this  point  or  property  is 
made,  pro  hac  vice , the  ground  or  basis  of  a classifi- 
cation. 

210.  But  by  the  very  nature  of  the  case  we  cannot 
make  an  assertion  without  referring  the  subject  of 

which  we  speak  to  a class  ; and  every  time  we 
menf Classifies  speak  of  it  in  a different  connection,  to  a 
new  class — the  differentia  of  which  is  ex- 
pressed by  the  predicate  we  use.  If  we  call  a man, 
brave  or  a coward,  honest  or  a knave,  wise  or  ignorant, 
good  or  bad,  polite  or  rude  ; — if  we  say  of  him,  he  is 
standing  or  walking,  sitting  or  sleeping,  all  these  classes 
are  called  up  before  the  mind,  and  every  new  assertion 
concerning  any  subject  of  which  we  are  speaking,  like  a 
fresh  turn  of  the  kaleidescope,  groups  and  classifies  all 
things  anew.  And  upon  this  classification  depends 
alike  the  cogency  of  an  argument,  the  merriment  of 
humor,  and  the  keen  relish  of  wit.  Even  a 
dicrous  cTaAfi-  jest  is  but  a ludicrous  classification.  A sar- 
casm does  no  more  than  to  class  one  with  per- 
sons and  things  that  are  contemptible,  and  a bad  name, 
a disgraceful  epithet,  a conviction  of  wrong,  brings 


n.] 


OF  PROPOSITIONS. SECT.  IV. 


55 


upon  one  only  the  differentia  of  the  species  to  which 
he  is  thus  referred. 


SECTION  IV. 

Of  the  Adequacy  of  Propositions. 

211.  Let  us  now  consider  some  of  the  principles 
and  laws  of  predication  with  reference  to  the  adequacy 
of  Propositions,  as  expressions  of  the  judgments  which 
they  represent. 

212.  A Proposition  for  the  purposes  of  Logic  should 
be  like  the  testimony  given  under  the  Com-  Adequacy  of 
mon  Law  oath  in  civil  suits,  “ the  truth , the  Pr°p°sitions- 
lohole  truth , and  nothing  hut  the  truth  A 

(l.j  Of  any  object  or  class  of  objects,  its  Name  and  De- 
uame  and  its  definition  may  ot  course  be  cated. 
predicated. 

(2.)  Synonymous  terms  may  also  always  be  predi- 
cated of  each  other.  But  any  two  or  more  synonymous 
names,  which  are  not  mere  individual  names,  Terms- 
and  which  may  be  predicated  of  the  same  object  of 
thought,  must  denote  Alternate  Conceptions  of  that 
object,  and  are  not  likely  to  be  predicable  of  each 
other. 

(3.)  Of  any  general  term,  that  is,  a term  denoting  a 
genus,  we  may  predicate  any  term  denoting  of  a Genus, 
the  essentia  of  the  genus,  or  any  one  of  the  essentia  in 
an  abstract  term,  or  by  a connotative  adjective. 

(1.)  Of  the  Species  we  may  in  the  same  way  predi- 
cate not  only  the  Essentia  of  any  higher  and  Essentia  of 
comprehending  genus,  but  also  its  own  Dif-  Species- 
ferentia. 

(5.)  Of  any  individual  we  may  also  in  the  like  way 
predicate  the  Essentia  of  any  genus  in«which  of  the  Indi 
it  is  included,  the  differentia  of  the  species  vidual- 
to  which  it  belongs,  and  the  peculiarities  of  the  indi- 
vidual (inseparable  accidents). 

(6.)  Whatever  may  be  predicated  of  each  individual 


56 


LOGIC. PAHT  I. 


[chap 


of  individuals  in  a class,  may  be  predicated  of  the  class 
as  a whole.  Thus  if  each  individual  man 
has  two  feet,  then  “ man  is  a two-footed  order  of 
beings.” 

213.  Besides  the  above  there  are  always  properties 
Accidental  pro-  which  are  not  regarded  as  either  Essentia  or 
labilT  pre  1 Differentia,  as  well  as  separable  accidents 
which  constitute  the  various  modes  or  conditions  of 
being,  that  may  be  predicated  of  any  subject  when- 
ever we  have  any  sufficient  reason  to  affirm  them  of  it. 

211.  If  the  subject  denotes  any  real  or  possible 
predicatea  of  tiling,  then  the  Predicate  may  be  a positive 
bie  subjects.  term  and  denotes  some  property  that  is  pre- 
dicated of  it.  For  if  it  be  a possible  or  a real  thing,  we 
can  say  “ it  is  possible,”  “ it  is  real.”  But  if  it  be  an 
impossible  thing  its  predicate  must  be  a negative  term, 
since  no  property  or  mode  can  exist  without  its  sub- 
stance ; thus  if  the  conception  denoted  by  the  subject 
A be  an  impossibility,  we  can  say  that  “ it  is  impossi- 
sible.” 

215.  Whenever  a given  predicate  is  to  be  used 
Alternate  con-  that  Alternate  Conception  of  the  subject 
ject3°'ls  dS  sub  should  be  used,  which  represents  it  by  the 
matter  on  account  of  which  it  is  contained  in  the  genus 
denoted  by  the  Predicate. 

216.  Alternate  Conceptions  represent  the  same  ob- 
ject by  different  matter.  But  the  subject  is  included 
in  the  sphere  of  the  Predicate,  only  because  it  has  the 
properties  which  constitute  the  Essentia  of  the  genus 
Examples.  denoted  by  the  Predicate.  Thus,  Washing- 
ton as  General  commanded  the  American  Army  ; gave 
Commissions  to  the  Officers  in  the  Army  and  Navy,  &c. 
But  as  President  he  presided  over  his  Cabinet,  nomi- 
nated Civil  Officers,  sent  Messages  to  Congress,  pos- 
sessed the  Veto"  Power.  But  it  would  be  logically 
faulty  to  say,  “ the  American  Commander  ate  his 
breakfast,”  for  instance  ; for  as  Commander  he  did  not 
eat,  but  it  was  simply  as  George  Washington  that  he 
ate.  So  it  should  not  be  said  of  an  act  in  his  military 


n.] 


OF  PROPOSITIONS. SECT.  IV. 


57 


command, — the  President  did  it ; for  as  President  he 
did  not  do  it,  but  only  as  Commander  did  he  do  it. 
Nor  should  we  say  George  Washington  vetoed  this 
bill,  for  not  as  George  Washington  but  as  President 
Washington  did  he  possess  the  veto  power,  or  exer- 
cise it. 

217.  Words  denoting  titles  and  ranks  are  however 
but  Alternate  Conceptions  of  the  individuals  Titles, 
to  Avhom  they  are  given,  and  custom  has  so  far  not  only 
sanctioned,  but  required  the  use  of  a man’s  title  even 
when  we  are  speaking  of  his  personal  acts  and  proper- 
ties, that  a disregard  of  the  usage  would  be  regarded 
as  discourteous  if  not  as  intended  for  an  insult. 

218.  The  subject  of  any  proposition  should  always 
be  so  comprehensive  as  to  include  all  the  comprehen 
individuals  to  which  the  predicate  used  m subject. 

the  proposition  is  applicable. 

219.  This  condition  is  often  violated  for  rhetorical 
purposes  ; nor  does  its  violation  necessarily  Rhetorical 
involve  an  error  in  the  conclusion,  though  it  violations, 
renders  us  liable  to  fall  into  one.  Thus  we  say  “ the 
Papists  hold  to  the  supremacy  of  the  Pope,”  which  is 
correct.  But  if  we  say  “ the  Papists  believe  in  the 
Divinity  of  Christ,”  we  say  what  is  indeed  true  ; but 
as  other  Christians  believe  in  that  dogma  also,  our  sub- 
ject is  of  too  narrow  a comprehension,  and  suggests 
the  inference  that  a belief  in  the  Divinity  of  Christ  is 
one  of  the  differentia  of  the  Papists.  Although  there- 
fore there  may  be  cases  in  which  the  violation  of  this 
rule  does  no  harm,  yet  unless  there  is  something  in  the 
context  or  iii  the  circumstances  under  which  the  rule 
is  violated  to  guard  against  the  error,  the  rule  must  be 
strictly  adhered  to,  or  our  proposition  does  not  state 
“ the  whole  truth.”  * 

* I have  before  me  a case  in  point.  In  an  infidel  author,  whom  I need 
not  name,  there  is  an  accumulation  of  statements  designed  to  show  that  the 
Scriptures,  as  we  now  have  them , cannot  be  relied  upon  as  inspired.  He  says 
of  the  Scriptures  (his  subject),  “ the  oldest  manuscript  does  not  reach  back 
to  within  centuries  of  the  origin  which  the  Scriptures  claim  for  themselves. 

3* 


58 


LOGIC. PART  I. 


[CHAP. 


220.  When  the  Predicate  is  a general  term  and  not 
a mere  connotative  of  some  accident  of  the  subject,  the 

pm  erties  of  accidents  of  the  subject  are  not  included  bj 
the  subject  in-  means  of  the  proposition  in  the  matter  of  the 
Predicate.  Thus  when  we  say,  “ the  rich 
are  anxious,”  we  take  no  notice  of  the  color, 
size,  or  any  other  accident  of  the  persons  included  in 
the  word  “ rich.”  If  we  say  “ John  is  sick,”  this  im- 
separai  i 5 Ac  P^es  n°thing  concerning  his  accidents,  and 
cidentaara0r  the  no  connection  of  the  Predicate  with  them ; 
eluded  fn°  the  the  Predicate  is  affirmed  of  what  is  essential 
to  the  subject  as  such  and  not  of  any  of  its 
accidents — that  is,  what  is  essential  to  it  as  a subject, 
and  not  what  is  necessary  to  its  reality.* 

221.  But  whatever  term  is  predicable  at  all  of  either 
individual  species  or  genus,  must  be  predicable  of  the 

individual  or  individuals  (if  the  subject  be 
must  include  either  a specific  or  generic  term),  as  contam- 
matter  of  the  mg  in  this  conception  whatever  is  necessary 
to  their  existence  as  individuals,  species,  or 
genus  as  the  case  may  be. 

222.  Thus  if  we  say  “ This  mountain  has  existed  since 
the  creation  of  the  world,”  we  are  understood  to  say 
not  merely  that  the  matter  of  which  it  is  composed  has 
existed  so  long,  but  that  that  matter  has  existed  not 

It  is  written  in  a letter  entirely  different,  now  divided  into  words,  surrounded 
by  points  indicative  of  the  meaning  and  punctuation  of  words,  divided  up 
into  chapters  and  verses,  and  the  manuscripts  abounding  in  various  readings, 
interpretations,  omissions,  and  corruptions.”  But  the  author  does  not  state, 
and  the  unlearned  reader  does  not  know,  that  precisely  the  same  thing 
could  he  predicated  of  the  text  of  Herodotus,  Thucydides,  Livy,  Tacitus, 
and  in  fact  of  every  ancient  author,  and  yet  no  one  ever  doubted  the 
genuineness  of  the  works  which  are  received  under  those  names  on  that 
account.  If  he  had  made  his  subject  as  comprehensive  as  the  Predicate 
would  allow,  and  included  these  works  with  the  Scriptures  in  his  Proposi- 
tion, it  would  have  destroyed  the  effect  which  he  designed  to  produce. 

* The  scholastic  writers  expressed  this  distinction  by  the  use  of  the  abla- 
tive pronoun  qua.  The  subject  qua  subject — this  expression  is  also  used  to 
distinguish  between  the  different  predicates  which  any  object  of  thought 
may  have  when  represented  by  its  Alternate  conceptions.  Thus  Washington 
qua  President  possessed  the  Veto  Power,  qua  Commander-in-Chief  gave 
Commissions  to  the  Officers  of  the  Army  and  Navy. 


n.] 


OF  PROPOSITIONS. SECT.  Y. 


59 


only  as  mountain  [the  species],  but  also  as  this  indi- 
vidual mountain  with  its  inseparable  accidents.  So 
when  we  say  “ men  are  immortal,”  we  mean  not  only 
that  what  is  essential  to  humanity,  but  also  whatever  is 
distinctive  of  each  individual  as  an  inseparable  acci- 
dent is  included  in  the  immortality ; so  that  men  will 
exist  there  individually,  distinct  and  distinguished  by 
the  same  inseparable  accidents  of  personality  as 
here. 

223.  For  rhetorical  purposes  this  rule  also  is  often 
violated.  In  all  those  figures  of  speech  called  Rhetorical  „i0. 
Metaphor,  Trope,  &c.,  these  rules  of  Logic  lat‘0QS- 
are  departed  from  for  rhetorical  purposes.  It  becomes 
necessary  therefore  to  consider  in  all  cases  whether  the 
word  used  is  the  real  subject,  or  merely  some  figure 
of  speech  used  in  its  stead. 

SECTION  V. 

Of  the  Quantity  of  Propositions. 

221.  The  scope  of  the  judgment  is  not  important  to 
its  deductive  force  or  position  in  a syllogism,  since 
whether  it  includes  much  or  little  in  a numerical  esti- 
mate it  goes  in  for  what  it  is. 

225.  But  the  Logical  Quantity  is  of  the  utmost 
importance, *since  that  indicates  its  relative  importance  of 
amount  and  determines  the  laws  of  predica  - Terms, 
tion  and  deduction. 

226.  Logical  Quantity  in  its  broadest  sense  is  of 

three  varieties, — (1)  comprehensive  ; (2)  in-  Three  Dimen- 
tensive  ; and  (3)  protensive.  Quantity. 

(1.)  Comprehensive,  or  Extensive  Quantity,  is  the 
comprehensiveness  of  the  sphere  of  the  con-  comprehen- 
ception. 

(2.)  Intensive  Quantity  is  measured  by  the  amount 
of  matter  in  the  conception.  intensive. 

(3.)  But  we  have  also  a Protensive  Quantity  brought 
in  by  the  consideration  that  the  facts  included  protensive. 


60 


LOGIC. PAKT  I. 


[chap. 


in  the  sphere  of  any  conception  are  not  always  actual 
facts  at  the  same  moment  of  time.  If  we  say  “ all  men 
are  mortal,”  we  mean  to  include  in  our  category  not 
only  all  men  now  living,  hut  all  who  have  lived  in  time 
past  or  will  live  in  time  to  come — all  beings  that  are 
men.  But  a predicate  may  be  ascribed  to  a subject  at 
one  time,  or  as  true  of  it  at  some  times,  which  could 
not  be  ascribed  to  it  with  truth  at  others. 

After  having  thus  named  this  variety  of  Quantity, 
we  shall  leave  it  out  of  consideration  for  the  present, 
and  proceed  to  consider  Comprehensive  or  Extensive 
Quantity  in  reference  to  judgments. 

227.  In  reference  to  the  object  now  before  us  Inten- 
intens.ve  Quan  sive  quantity  is  unimportant  in  itself,  and  is 

tity  determined  ^ i 

hensive^ompre  a*ways  determined  by  tlie  Comprehensive 
quantity  being  always  in  the  inverse  ratio 
sumedasabso^  1°  ib  The  Protensive  quantity  is  assumed 
lute-  to  be  absolute  ; that  is,  to  include  all  time — 

and  the  same  as  if  it  were  expressed  by  the  word 
“ always ,”  as  “ All  A is  always  B ; ” “ Men  are  always 
mortal.” 

228.  There  are  three  dimensions  of  Comprehensive 
Three  pimen-  Quantity,  according  as  the  subject  of  a judg- 
prehensive om"  ment  may  be ; — (1)  an  individual ; (2)  several 

individuals  considered  as  a part  of  a class, 
not  denoted  by  any  term  which  constitutes  them  a 
species  within  that  class ; or  (3)  several  individuals  con- 
sidered as  constituting  a class,  species,  or  genus. 

229.  The  first  class  are  called  Individual  judg- 
ments ; the  second  Particular  j udgments ; and  the 
third  are  called  Universal. 

230.  It  is  obvious  that  on  these  principles  of  divi- 
sion, and  in  reference  to  Quantity,  there  can  be  but 
three  Species  ; for  a judgment  must  be  either  of  one , 
of  some,  or  of  all.  If  we  say  that,  “ some  ” may  in- 
clude many  or  only  a few  ; nearly  all  or  only  two ; we 
do  not  thereby  constitute  a Logical  whole. 


n.] 


OF  PROPOSITIONS. — SECT.  VD.  . 


61 


SECTION  VI. 

Of  the  Quality  of  Judgments. 

231.  The  Copula  of  a Judgment  may  be  either 
(1)  affirmative,  or  (2)  negative;  that  is,  we  .Three  Qunii. 
may  say  A (is)  B,  or  A (is  not ) B.  The  first  t!onSof  FropOM' 
A is  B,  includes  A in  the  sphere  of  B,  and  is  an  Affirma- 
tive judgment ; the  second  A is  not  B,  excludes  A from 
the  sphere  of  B,  and  is  a Negative  judgment.  But  B 
and  not-B  are  antithetic  terms.  They  denote  spheres 
which  are  the  complements  of  each  other.  Hence  if 
A is  not  in  the  sphere  of  B,  it  is  in  the  sphere  of  non-B  ; 
and  we  may  say  that  A is  non-B.  This  is  called  (3)  an 
Indefinite  judgment.  Hence  three  varieties  in  refer- 
ence to  Quality — 1st,  includes  the  subject  in  the  sphere 
of  the  Predicate ; 2d,  excludes  the  subject  from  the 
sphere  of  the  Predicate  ; the  3d,  includes  the  subject 
in  the  Negative  sphere  connoted  by  the  Predicate  of 
the  Affirmative. 

It  is  obvious  that  in  reference  to  Quality  there 
can  be  no  other  species  of  judgments  than  these 
three. 

SECTION  VII. 

Of  the  Modality  of  Judgments. 

232.  In  reference  to  the  certainty  of  the  Judgment, 
we  may  have  three  kinds  of  judgments  Three  Modes 
Problematical , Assertive , and  Necessary , or  ofProSS^lons- 
Ajpodictical.  This  is  called  the  Modality  of  Judg- 
ments. 

(1.)  The  Differentia  of  the  Problematical  is  that 
they  merely  affirm  that  the  subject  may  be  Problematical, 
in  the  category  of  the  Predicate,  or  the  possibility  of 
the  Proposition  being  true. 

(2.)  The  second  is  called  Assertive  ; — they  affirm 
the  truth  of  the  judgment  as  a matter  of  fact 
and  reality. 


Assertive. 


62 


LOGIC. PART  I. 


[CRAP. 


(3.)  The  third  are  called  Necessary  or  Apodictical  ; 
Necessary.  they  affirm  that  the  truth  could  not  be  other- 
wise— as  when  we  say  “ two  and  two  make  four.” 


SECTION  VIII. 


Of  the  Four  Cardinal  Propositions. 


233.  Combining  Quantity,  Quality,  and  Modality, 
Twenty-seven  we  have  the  following  table  of  Categoric 

'ntnrmripfl  1 _ ^ O 


Categorical 

Judgments. 


Judgments. 


Individual 


Categoric  Particular 


Universal 


Affirmative 

- Negative 
Indefinite 
Affirmative 

- Negative 
Indefinite 
Affirmative 

- Negative 
Indefinite 


Problematic. 

Assertive. 

Apodictic. 

Problematic. 

Assertive. 

Apodictic. 

Problematic. 

Assertive. 

Apodictic. 

Problematic. 

Assertive. 

Apodictic. 

Problematic. 

Assertive. 

Apodictic. 

Problematic 

Assertive. 

Apodictic. 

Problematic. 

Assertive. 

Apodictic. 

Problematic. 

Assertive. 

Apodictic. 

Problematic. 

Assertive. 

Apodictic. 


II.] 


OF  PROPOSITIONS. SECT.  VIII. 


63 


234.  But  as  Problematical  judgments  never  enter 
as  Premises  into  any  Argument  merely  as  Problema- 
tical, we  may  omit  them  from  any  further  consideration 
at  present. 

235.  Again  the  difference  between  the  Assertive 
and  the  Apodictic  or  Necessary  has  no  effect 

upon  the  general  principles  ot  deduction,  dais  reduced  to 
If  a Proposition  be  true,  that  is  all  that  is 
required,  the  modality  of  its  truth  being  wholly  unim- 
portant. We  may  take  the  Assertive  therefore  for  all 
our  purposes,  neglecting  the  difference  between  that 
and  the  Necessary. 

236.  But  again,  the  Negative  and  the  Indefinite 
sub-species  are  the  same  so  far  as  all  the 

laws  ancl  purposes  oi  deduction  are  con-  nties  reduced  to 
cerned.  For  since  the  Positive  and  the 
Negative  Spheres  are  complements  of  each  other,  to 
exclude  from  the  Positive  (which  is  the  differentia  of 
the  Negative)  is  the  same  as  the  inclusion  in  the 
Negative  sphere  (which  is  the  differentia  of  the  Inde- 
finite). 

237.  Again  in  respect  to  Quantity  the  Individual 
and  the  Universal  are  alike,  in  that  the  sub- 
ject (in  which  alone  is  found,  the  differentia  Quantities  7e- 
of  Quantity)  is  in  both  of  them  a logical  duct'd  t0 t"°- 
whole.  Whether  an  individual  or  a class,  it  is  imma- 
terial for  all  the  purposes  of  deduction,  so  long  as  it  is 
a logical  whole.  Hence  we  consider  Individual  judg- 
ments the  same  as  Universal  for  all  the  purposes  of 
deduction. 

238.  But  a Universal  Judgment  may  be  either 
Negative  or  Affirmative,  and  so  likewise 

may  a Particular  judgment.  We  have  only  Q?arnytltycom. 
four  cardinal  judgments  which  we  need  con-  ine  ' 
sider.  These  are  Universal  Affirmative,  Universal 
Negative,  Particular  Affirmative,  and  Particular 
Negative.  These  may  be  considered  the  four  cardinal 
Propositions  in  Logical  Quantity. 

239.  As  these  occur  so  often,  writers  on  Logic  have 


LOGIC. — PART  I. 


64 


[chap. 


generally  designated  them  by  the  first  four  vowels  of 
the  Alphabet.  Thus 

U.  A.  All  A is  B,  is  represented  by  A 

U.  IST.  No  A is  B “ “ “ E 

P.  A.  Some  A is  B is  “ “ I 

P.  N.  Some  A is  not  Bis  “ “ O 


These  are  all  Categorical,  all  Assertive,  and  differ  only 
in  Quantity  and  Quality. 


SECTION  IX. 

Of  the  Distribution  of  Terms. 

240.  When  a term  is  taken  into  the  scope  of  a 
judgment  as  a logical  whole,  it  is  said  to  be  distributed 
in  the  judgment ; hut  if  it  does  not  enter  in  as"  a 
logical  whole,  it  is  said  to  be  undistributed  in  the 
judgment. 

241.  It  is  immaterial  whether  the  part  of  the  whole 
undistributed  be  a large  or  small  part,  “ many  ” or  u few ; ” 

and  these  words  therefore  indicate  an  undis- 
tributed term  as  well  as  “ some.” 

242.  So  also  we  may  say  “ some,”  when  we  mean 
“ some  at  least  and  possibly  all ; ” or  when  we  mean 
“ some  hut  not  the  whole.”  But  the  undistributed 
term  as  such  indicates  nothing  of  the  kind,  and  if  any 
such  modification  of  the  term  is  intended,  the  Proposi- 
tion expressing  it  becomes  a compound  one  [either 
copulative  or  discretive],  expressing  two  judgments 
in  fact  and  not  one  merely. 

243.  The  conception  represented  by  an  undis- 
tributed term  is  not  a logical  whole,  and  the  term  itself 

Not  Logical  must  necessarily  be  a general  one.  But  if 
wholes.  the  term  denotes  a part  of  the  whole,  con- 
ceived as  a species , it  is  no  longer  undistributed ; for 
the  part  conceived  as  a species  becomes  by  the  very 
fact  of  its  being  so  conceived  a logical  whole. 

244.  Hence  the  word  “ some”  though  generally 


n.] 


OF  PROPOSITIONS. SECT.  IX. 


65 


used  to  denote  an  undistributed  term  in  the  subject, 
is  not  an  infallible  indication  that  the  term  is  undis- 
tributed. Thus  in  the  illustration  given  b j Mistake  Gf the 
Sir  William  Hamilton,  “ some  stars  are  all  forceof  “some  ” 
planets  ” (all  the  planets  are  stars).  But  one  must  have 
a conception  of  those  stars  as  a class,  which  are  planets, 
and  as  distinguished  by  the  differentia  of  planets,  or  he 
could  not  say  that  they  were  all  the  planets  that  there 
are  among  the  stars.  If  therefore  there  ever  was,  or 
ever  should  be  such  a Proposition,  except  when  got  up 
for  the  purpose  of  seeing  what  one  can  do,  the  subject 
must  be  regarded  as  distributed,  notwithstanding  the 
usual  signs  of  an  undistributed  term. 

215.  There  are  three  ways  of  ascertaining  whether 
a term  is  distributed  or  used  distributively  Three  ways 

. ...  . \ -r-v  . i d of  distribution 

m any  proposition  or  not. — (1)  By  the  nature  of  terms, 
of  the  term ; (2)  by  a modal  sign ; and  (3)  by  its 
position. 

446.  A term  is  distributed  by  its  nature  when  it  is 
used  to  denote  any  individual  object,  such  By  the  nature 

,r  l J c 7 of  the  term. 

as  j^roper  names  oi  persons,  places,  &c. 

Terms  are  distributed  by  signs  in  three  By  signs, 
ways. 

24:7.  (1.)  The  particles  “ the,”  “ this”  “ that”  by 
pointing  out  a particular  individual  in  a class,  ..xhe>„  “th,v 
of  which  the  predicate  is  affirmed,  make  the  and  “ that-” 
term  distributed  ; since  the  force  of  these  particles  is  to 
include  only  the  one  of  the  individuals  comprehended 
within  the  genus  thus  pointed  out  in  the  scope  of  the 
j udgment. 

248.  (2.)  Such  words  as  “ all,”  “ every”  &c.,  dis- 
tribute the  terms  ; in  fact  they  are  the  most  <.A1I„  ..eve, 
usual  signs  of  a distributed  term  used  in  the  ry”  &c- 
subject  of  a Proposition. 

249.  “ All  ” of  course  clearly  and  expressly  includes 
all  of  the  individuals  included  in  any  genus  within  the 
scope  of  the  judgment. 

250.  As  “ all,”  so  also  “ every  ” indicates  a dis- 
tributed term,  since  it  necessarily  includes  all  the  indi- 


66 


LOGIC. PAJRT  I. 


[CHAP. 


viduals  of  the  logical  whole  within  the  scope  of  the 
Difference -be  J udgment.  All  is  indeed  sometimes  a col- 
and^Every1””  ^ec^tve  ra^ier  than  a distributive  sign.  Thus 
'Lry  if  we  say  “ all  these  trees  make  a fine  shade,” 
it  is  most  likely  that  we  mean  to  take  “ trees  ” as  a 
collective  term  rather  than  as  a general  term  ; that  we 
have  predicated  of  them  taken  together  as  a collective 
whole,  what  could  not  be  predicated  of  each  of  them 
individually.  This  difference  is  unimportant  to  the 
purposes  now  before  us,  but  it  will  be  seen  by  and  by 
that  it  lies  at  the  bottom  of  a most  serious  fallacy. 

251.  (3.)  Two  pronouns,  as  “ he  who,”  and  “ they 
two  pronouns  that,”  are  clearly  indicative  of  a distributed 

distribute  the  , ,,  7 u 7 . . 

subject.  subject,  as  “ he  who  transgresses  the  law 
commits  a sin,” — “ who  so  transgresses  the  law  com- 
mits sin  ; ” these  forms  of  Propositions  clearly  include 
the  whole  class  denoted  by  the  specific  term,  whose 
differentia  is  given  in  the  words  “ transgresses  the 
law,”  in  the  scope  of  the  judgment. 

252.  (4.)  Again,  we  have  another  class  of  signs, 
which,  although  they  do  not  cause  the  general  term  to 
be  included  as  a whole  in  the  scope  of  the  judgment, 
constitute  it  what  is  called  a distributed  term.  These 

“ Each”  and  terms  are  such  as  “ each”  “ any  • ” for  while 
“Any.”  py  t]ie;r  force  they  apply  the  predicate  of 
the  proposition  to  one  individual  of  a class  only,  and 
sometimes  in  such  a way  as  that  it  can  be  applied  to 
one  only  at  the  same  time,  yet  they  imply  that  before 
any  actual  predication  it  is  applicable  to  them  all  and 
every  one  of  them  taken  individually,  although  it  may 
cease  to  be  so  the  moment  it  has  been  predicated  of 
one.  Thus  if  we  say  of  a young  lady,  “ any  man 
would  marry  her  ; ” — <£  man  ” must  be  taken  as  a dis- 
tributed term,  though  it  is  not  supposed  that  more  than 
one  man  will  actually  marry  her. 

253.  (5.)  The  indefinite  article  “ a”  also  sometimes 

The  indefinite  distributes  the  subject  in  the  same  way,  thus 
"a.”  u a poison  destroys  life  ; ” that  is,  “ any  poi- 

son,” or  “ all  poisons  destroy  life.” 


II.] 


OF  PROPOSITIONS. SECT.  IX. 


67 


254.  In  all  Negative  Propositions  the  Predicate  is 
taken  as  a Whole.*  The  differentia  [charac-  By  position  the 
teristic]  of  Negatives  is  that  they  exclude  Negate  judg- 
the  subject  from  the  sphere  of  the  Predicate.  ments- 
They  do  not  merely  partly  exclude  it,  they  may  exclude 
merely  a part  of  the  subject,  but  they  must  exclude  the 
subject  whether  §s  a whole  or  as  a part  from  the  whole 
of  the  Predicate,  “ No  vice  is  commendable.”  If  now 
among  all  the  things  that  are  commendable  one  vice 
can  be  found,  the  Proposition  is  not  true.  Hence  it 
distributes  the  Predicate  or  speaks  of  it  as  a whole. 
Or  if  we  say  “ some  men  are  not  brave,”  which  is  a 
Proposition  in  O,  the  same  is  found  to  be  the  case 
with  the  Predicate.  We  here  mean  that  among  all 
the  things  that  are  “ brave,”  the  “ some  men,”  are 
not  included. 

255.  But  the  Affirmatives  do  not  necessarily  dis- 
tribute the  Predicate.  If  I say  that  A is  B, 

all  that  is  affirmed  thereby  is  that  A is  in  B,  not  rmdktlfbute 
or  A is  some  part  of  JB.  A is  included,  m 
the  sphere  of  B.  But  B may  include  much  besides  A. 
“ Men  are  mortal ; ” but  men  are  not  the  only  things 
that  are  mortal.  The  sphere  of  “ mortal  ” is  not  coin- 
cident and  identical  with  that  of  “ man,”- — it  is  much 
more  comprehensive.  Hence  in  A we  do  not  speak 

* Sir  William  Hamilton  in  his  new  method  of  Notation,  insists  that  there 
may  be  Negative  Judgments  with  undistributed  Predicates. 

But  besides  the  proof  given  in  the  text  of  the  position  there  taken,  we 
may  say  further  that  his  doctrine  directly  contradicts  the  old  axiom,  “ it  is 
impossible  for  a thing  to  be  and  not  to  be  at  the  same  time.”  For  suppose 
S is  not  P and  P not  taken  as  a whole,  the  sphere  of  P as  of  any  term  is 
determined  by  its  matter  ; and  the  subject  S is  included  in  it  if  it  possesses 
the  matter  of  P and  excluded  from  it  if  it  does  not.  Now  suppose  that  S 
has  not  the  matter  of  that  part  of  P which  we  take  into  the  scope  of  our 
judgment,  when  we  say  S is  not  P,  and  the  judgment  S is  not  P is  true. 
But  suppose  it  has  the  matter  of  the  part  of  P,  not  taken  into  the  scope  of 
the  Negative  judgment,  and  then  we  have  S is  P ; — 

that  is,  S is  not  P, 

S is  P, 
and  P is  P, 
and  P_is  not  P. 


68  LOGIC. — PART  I.  [CHAP. 

of  the  predicate  as  a whole.  The  predicate  is  undis- 
tributed. 

256.  For  the  same  reason  we  do  not  speak  of  the 

Predicate  as  a whole  in  I.  “ Some  men  are  black  ; ” 
we  do  not  speak  of  “ black  things  ” as  an  entire  class, 
comprehending  no  more  than  the  “ some  men  ” of 
whom  we  were  speaking.  # 

257.  Hence  the  following  Rules  for  the  Distribution 
Rules.  of  Terms  by  position. 

1.  All  universal  Propositions  distribute  the  Subject. 

2.  All  negative  Propositions  distribute  the  Predi- 
cate. 

Or  more  definitely : 

A distributes  the  subject. 

E “ both  the  subject  and  predicate. 

I “ neither. 

O “ the  predicate  only. 

258.  Various  devices  have  been  resorted  to,  to  repre- 
iiiustrations.  sent  by  some  diagram  these  various  Judg- 
ments or  Propositions.  Many  of  them  are  ingenious 
and  useful,  but  all  are  liable  to  misapprehension,  aris- 
ing from  the  nature  of  the  case  and  the  difficulty  of 
representing  any  mere  conception  by  actual  forms. 

The  following  is  perhaps  as  good  as  any  that  can 
be  given.  It  is  substantially  Euler’s  : — 

A. — All  S is  P,  in  which  case 
one  circle  S is  included  wholly  in 
the  other  as  P,  but  does  not  oc- 
cupy the  whole  of  its  sphere. 

E. — Ho  S is  P,  in  which  case 
one  circle  S is  wholly  excluded 
from  the  whole  of  the  other  P. 

I.— Some  S is  P,  in  which  case 
we  have  two  incomplete  circles 
S and  P,  cutting  each  other  so 
as  to  have  a part  x common  to 
both. 


II.] 


OF  PROPOSITIONS. SECT.  X. 


69 


O. — Some  S is  not  P,  in  which 
we  have  an  incomplete  circle,  S 
not  included  in  any  part  of  the 
complete  circle  P. 

259.  One  difficulty  attending  the  above  diagrams 
is,  that  they  represent  in  A and  I the  sub-  Dan„er  of 
ject  as  constituting  a definite  part  of  the  using them- 
Predicate,  or  occupying  an  ascertained  portion  of  its 
sphere,  whereas  the  judgment  does  not  so  represent 
the  spheres. 

260.  It  will  be  noticed  that  in  A when  the  sphere 
of  S becomes  so  large  as  to  fill  up  and  occupy  . The  predicate 
the  whole  of  P,  the  Predicate  has  become  d?stfi*™dUve9 
distributed  and  is  taken  as  a whole.  The  spheres  are 
then  coincident  and  identical. 

SECTION  X. 

Of  Immediate  Inference. 

The  form  Judgments  expressed  by  the  Proposi- 
tions A,  E,  I and  O,  which  we  have  just  examined, 
have  certain  relations  to  each  other  which  it  is  impor- 
tant to  examine. 

261.  Such  is  the  relation  of  judgments  to  each 
other,  that  no  judgment  can  be  true  without  Every  Judg. 
implying  the  truth  of  some  other  judgment,  “neonther.implie3 
either  in  the  same  or  in  the  opposite  Quality. 

262.  These  judgments  which  are  thus  inferred  from 
others,  as  from  All  A is  B,  we  infer  that  Irnme<]iate  in- 
some  A is  B,  and  that  “ some  A is  not  B ” ference- 

is  not  true,  are  called  by  Ivant  “ Syllogisms  of  the  Un- 
derstanding.” I shall  prefer,  however,  to  adopt  the 
more  English  name  of  Immediate  Inference. 

263.  I call  it  “ immediate  ” because  the  inference 
or  conclusion  is  drawn  without  the  interven-  why  so  called, 
tion  of  that  medium  or  middle  term,  which  is  always 
necessary  in  the  complete  Syllogism,  as  will  be  seen 
hereafter, 


70 


LOGIC. PAKT  I. 


[chap. 


264.  By  Immediate  Inferences  then  I mean  all  those 
inferences  or  conclusions  that  can  he  drawn  from  any 
Proposition  without  the  intervention  of  any  other  matter 
or  term  than  was  given  in  the  Proposition  itself.  And 
as  it  will  be  the  most  convenient  to  point  out  these 
Inferences  as  we  examine  the  Opposition,  Permutation, 
and  Conversion  of  Propositions  (since  it  is  by  these 
means  that  the  Inference  is  made),  I will  keep  them 
in  mind  as  a subordinate  object  while  discussing  these 
topics. 


I.  Of  the  Opposition  of  Judgments. 

265.  (1.)  A and  E being  Universals,  I and  O are 
subalterns.  called  in  reference  to  A and  E their  Subal- 
terns. I being  subaltern  to  A and  O to  E. 

(2.)  A and  E in  relation  to  each  other  are  Con- 

Contraries.  tVCLVicS. 

sub-contraries.  (3.)  I and  O are  Sub-contraries. 

266.  (4.)  E and  I as  likewise  A and  O are  Contra- 
contradictories.  clictories  to  each  other. 

267.  If  now  a Universal  be  true  its  Subaltern  must 
be  true  also.  If  All  A is  B,  Some  A is  B,  is  true  as  an 
inference  from  Immediate  Inference,  and  if  the  Subaltern 
subalterns.  be  true  the  Universal  as  a Problematical 
Judgment  is  true  also,  as  an  Immediate  Inference  ; that 
is,  If  Some  A is  B,  all  A may  be  B. 

268.  Of  the  Contrmdes  only  one  can  be  true  in  the 
From  contraries,  same  matter,  though  both  may  be  false. 
Hence  If  A is  true  E is  false  as  an  Immediate  Infer- 
ence, and  vice  versa;  that  is,  Ho  A is  B,  then  All 
A is  B is  untrue,  although  of  course  Some  A may 
be  B. 

269.  Of  Contradictories  both  cannot  be  true  or  false 
From  contra-  in  the  same  matter.  Hence  If  E is  false  I 

must  be  true,  and  vice  versa.  If  A be  false 
O must  be  true,  and  if  I be  false  E must  be  true,  and 
if  O be  false  A must  be  true  as  Immediate  Infer- 


ence. 


II.] 


OF  PROPOSITIONS. SECT.  X. 


71 


270.  The  Sub-contraries  may  both  be  true  in  the 


same  matter.  If  some  A is  B,  some  A is 


Sub-contraries 
cannot  both  be 
false. 


A contraries  E 


co  C '//  A>  m P, 

HO-  VI,  -V°  H C“ 

S p,  S s> 

•o  ~ E? 

n 2 o,  3 2 

3 c°  % t=  3 

I sub-contraries  0 


not  B,  may  also  be  true. 

271.  But  the  Sub-contraries  cannot  both  be  false  in 
the  same  matter. 

272.  We  may  represent  the  rela- 
tion of  these  four  Judgments  by  the 
following  diagram,  in  which  it  will 
appear  that  the  sub-contrary  of  any 
subaltern  is  the  contradictory  of  its 
Universal ; and  if  therefore  two  con- 
tradictories cannot  be  false  at  the  same  time,  then 
a fortiori  the  two  sub-contraries  cannot. 

273.  The  subject  in  each  of  the  sub-contraries  is 
undistributed,  and  the  more  nearly  it  ap-  RatioofQua. 
proaches  to  the  Universal  in  one  quality  in  llty- 

any  case,  so  much  the  more  nearly  does  it  approach  it 
in  the  other.  Thus  the  more  nearly  Some  A is  B is  to 
All  A is  B,  so  the  more  nearly  is  Some  A is  not  B to 
No  A is  B. 


II.  Of  Contra-Position  or  Permutation  of  Quality. 

274.  The  same  judgment  may  be  stated  in  either 
quality,  Affirmative  or  Negative  as  we  choose,  by 
means  of  Negative  terms  and  copulas. 

275.  In  reference  to  this  fact  we  will  call  the  first 
form  in  which  a judgment  is  stated,  or  rather  that  form 
which  states  the  judgment  in  the  Proposition  of  the 
same  quality  as  the  judgment  itself,  the  JEx- 

posita  / and  that  form  of  the  Proposition  contra‘pos!ta 
which  states  it  in  the  other  quality,  the  Con-  1 ermutatIon- 
tra-posita  ; and  the  change  itself  we  call  Contraposi- 
tion or  Permutation. 

276.  Thus  let  us  suppose  in  the  first  place  that  we 
have  the  Negative  Proposition  “ A is  not  B,”  illustration, 
or  “ No  A is  B.”  In  this  case  we  have  simply  ex- 
cluded A from  the  sphere  of  B,  and  thus  denied  of  it 
the  matter  of  the  conception  B.  But  since  the  Negative 


72 


LOGIC. — PAKT  I. 


[chap. 


of  B or  non-B  is  the  complementary  sphere  of  B,  what- 
ever is  not  in  B is  in  non-B,  and  consequently  whatever 
has  not  the  Essentia  of  B must  have  that  (if  there  is 
any)  of  non-B.  Hence  “ A is  not  B ” is  equivalent 
to  “ A is  non-B,” — “ non-B  ” being  a Negative  term  ; 
and  But  A is  non-B  is  an  Affirmative  Proposition  with 
a Negative  Predicate. 

277.  Hence  from  a Negative  Exposita  with  an 
Affirmative  Predicate  we  may  always  permute  into 
Contra-posita,  by  substituting  for  the  Positive  Predi- 
cate its  Privative  or  Negative,  and  dropping  the  Nega- 
tive from  the  Copula.  Thus  “ if  man  is  not  wise,”  he  is 
“ -imwise  ; ” if  he  is  “ not  free  ” he  is  a u slave.” 

278.  But  if  the  Predicate  is  a Negative  or  a Priva- 
Negative  or  tive  term  in  the  Exposita,  we  have  to  substi- 

dicate've  rL  tute  for  it  its  Affirmative,  and  drop  the 
Negative  from  the  Copula  also.  Thus  we  may  say  that 
“ Centaurs  are  not  impossible,”  then  “ Centaurs  are 
possible.” 

279.  The  same  holds  true  of  the  subject  when  the 
Predicate  denotes  a reality  and  not  a possible  only. 

when  true  of  We  may  substitute  for  the  subject  its  anti- 
the  subject.  tlietic  in  the  opposite  Quality  by  dropping 
the  negative  from  the  copula,  always  remembering  that 
the  term  substituted  is  an  undistributed  term. 

280.  But  since  no  property  or  mode  can  exist  or  be 
real  without  its  substance,  the  Predicate  may  denote  a 
property  which  has  no  existence.  In  that  case  there 
can  be  no  Contra-posita  by  means  of  the  negative  sub- 
ject ; thus  if  one  should  say  “ horses  are  not  Centaurs,” 
we  could  not  therefore  say  “ some  not-liorses  are  Cen- 
taurs,” for  this  would  imply  the  reality  of  “ Centaurs.” 

281.  But  if  the  Predicate  be  a reality  at  all  we 
may  always  say,  if  A is  not  B some  non-A  is  B. 

Let  “ holy  ” be  the  Predicate  and  “ man  ” the  Sub- 
uiustration.  ject,  “ no  man  is  holy,”  or  in  the  other  form 
“ all  men  are  not  holy.” 

If  now  we  connect  the  negative  with  the  subject 
“ no-man,”  this  is  no  longer  the  same  term  taken  in  a 


n.] 


OF  PROPOSITIONS. SECT.  X. 


73 


different  sense,  but  it  is  a totally  distinct  term.  It  in- 
cludes nothing  that  was  included  in  the  first  term 
“ man”  and  precisely  all  that  was  not  included  in  it. 
It  includes  whatever  is  not  “ man.”  Of  these  things 
manifestly  not  all  are  holy,  although  if  there  be  such 
a thing  as  holiness,  and  if  it  do  not  belong  to  man,  it 
must  belong  to  something  that  is  not  man.  Hence  we 
may  say  “ some  not-man  is  holy.” 

282.  If,  however,  we  connect  the  negative  with 
“ holy,”  and  say  “ All  men  are  not-holy  or  unholy” 
the  term  represents  an  entirely  different  cognition  from 
the  term  “ holy.”  But  the  new  term  must  be  regarded 
as  undistributed,  for  we  do  not  mean  to  say  that  man 
is  all  that  is  “ not  holy,”  or  that  whatever  is  “ not 
holy  ” is  “ man.”  And  yet  if  our  first  Proposition  is 
true  “ some  thing  not  holy  ” is  “ man.” 

283.  In  the  use  of  intelligible  signs  we  may  use 
the  Privative  instead  of  the  Negative  in  the  PrivatLve  used 
Predicate,  since  the  nature  of  the  subject  tf°™ SetheNpre- 
limits  the  range  of  the  thought  or  judg-  dicate- 
ment  to  the  proximate  genus.  Thus  for  “ man  is  not 
holy,”  we  may  substitute  the  privative  Predicate,  and 
say  “man  is  unholy ; ” the  subject  “man”  limiting 
the  scope  of  the  judgment  to  the  proximate  genus  to 
which  the  capacity  for  holiness  is  an  essentia,  and  also 
a differentia  in  the  next  higher  subaltern  genus. 

281.  But  when  we  change  the  Quality  by  changing 
the  subject  we  may  not  use  the  Privative,  ButnoUnthe 
since  there  can  be  no  a priori  necessity  that  Subject-# 
the  Predicate  should  be  predicable  of  some  one  indi- 
vidual in  the  proximate  genus  to  the  subject,  or  in 
any  genus  below  the  summum  or  absolute  whole  of 
realities. 

285.  If  the  Exposita  be  Affirmative  we  change  the 
quality  by  means  of  two  negatives — two  Perrnutation 
negatives  in  English  making  an  affirmative.  °f  Affirmatives. 

286.  This  change  of  the  quality  of  Affirmatives  by 
means  of  two  negatives  may  be  effected  in  three 
ways. . 


4 


74 


LOGIC. — PART  I. 


[CHAP. 


(1.)  With  two  negative  copulas,  as  “ there  is  no  A 
ist  case.  that  is  not  B,”  consequently  All  A is  B. 
Thus  “ there  is  no  man  without  [that  has  not\  sin,”  or 
“ all  men  are  sinners.” 

(2.)  The  second  form  is  wTith  a negative  copula  and 
2ti  case.  a negative  Predicate.  “ All  A is  not  non-B,” 
or  “ ISTo  A is  non-B  ; ” as  “ No  earthly  creature  is  im- 
mortal.” 

287.  In  this  case  the  whole  of  the  subject  is  ex- 
cluded from  the  Negative  sphere,  and  must  therefore 

privative  for  be  included  in  the  Positive  which  connotes 
Negative  sphere.  qie  Negative.  A Privative  term  will  answer 
just  as  well  as  the  Negative,  since  the  subject  always 
confines  the  judgment  to  objects  included  within  its 
own  sphere,  which  becomes  for  this  purpose  a proxi- 
mate genus,  of  which  the  Positive  Predicate  and  its 
Privative  are  the  coordinate  parts. 

(3.)  By  a negative  copula  and  a negative  subject 
3d  case.  used  distributively,  we  have  I by  contra- 
position. As  “ No  one  who  has  not  enough  is  rich.” 
Here  “ one  who  has  not  enough,”  or  “ all  who  have 
not  enough,”  is  a negative  term,  and  the  judgment  is 
the  same  as  “ some  [perhaps  all]  who  have  enough  are 
rich  ” (see  277). 

288.  This  form  however  states  something  more  than 
I,  since  it  would  never  appear  from  the  fact  that 
“ some  who  have  enough  are  rich,”  that  “ no  one  who 
has  not  enough  is  rich.” 

•289.  The  course  of  this  investigation  shows  that 
we  may  always  have  from  any  Exposita  its  contra-posita 
by  Immediate  Inference. 

III.  Of  the  Conversion  of  Propositions. 

290.  By  the  Conversion  of  Propositions  we  change 
conversion.  the  relative  place  of  Subject  and  Predicate, 
as  from  A is  B to  B is  A. 

291.  In  the  Conversion  of  Propositions,  the  first  form 
Exposita  and  we  call  Exposita , and  the  second  the  Con- 

Converse.  -*■ 

verse. 


n.] 


OF  PROPOSITIONS. SECT.  X. 


75 


292.  The  fundamental  canon  which  governs  the 

Conversion  of  Propositions  is  this  : Fundamental  canon. 

No  term  may  be  distributed  in  the  Converse  which 
was  not  distributed  in  the  Exposita. 

293.  As  E and  I are  alike  in  reference  to  the  distri- 
bution of  their  terms,  one  distributing  both  conversion  of 
and  the  other  distributing  neither  — their  EandI- 
conversion  takes  place  in  the  same  way  ; that  is,  sim- 
ply, No  A is  B,  therefore  No  B is  A.  Some  A is  B, 
therefore  Some  B is  A. 

Exposita , No  quadrupeds  have  wings,  therefore 

Converse,  No  winged  animals  are  quadrupeds. 

Exposita , Some  Poets  are  Americans,  therefore 

Converse,  Some  Americans  are  Poets. 

294.  This  is  called  Simple  Conversion , and  hence 
the  Buie,  when  both  Subject  and  Predicate  si;npie  con- 
are  distributed,  and  when  neither  are  dis-  version- 
tributed  the  Proposition  may  be  converted  simply. 

295.  But  in  A the  Subject  and  not  the  Predicate  is 
distributed.  Hence  we  cannot  convert  sim-  conversion  by 
ply  if  we  say,  “ all  American  citizens  are  nmitation- 
free,”  we  cannot  say  that  therefore  “ all  freemen  are 
American  citizens.”  We  must  limit  the  subject  and 
say,  therefore  “ some  freemen  are  American  citi- 
zens.” 

296.  This  is  called  conversion  by  limitation  or  per 
accidens. 

297.  A,  however,  when  stated  by  contra-position, 
may  he  converted  simply.  Thus  All  A is  B,  A by  contra. 
No  A is  non-B,  therefore  No  non-B  is  A.  gesitiocnonve“ed 
If  the  whole  of  A is  in  the  sphere  of  B,  simply- 
nothing  which  is  not  in  B can  a fortiori  be  in  the 
sphere  of  A. 

298.  O,  cannot  be  converted  except  by  first  chang- 
ing its  quality.  This  we  may  do  by  connect-  conversion  of 
ing  the  Negative  with  the  Predicate  by  °- 
which  we  permute  it  into  I.  And  then  of  course  it 
may  be  converted  simply.  Thus  “ Some  A is  not  B, 
therefore  Some  Not-B  is  A.” 


76 


LOGIC. PART  I. 


[CHAP. 


Exposita , Some  brave  men  are  not  soldiers, 
Converse , Some  not-soldiers  are  brave  men. 

299.  Hence  we  may  convert  E and  I simply.  A by 
limitation,  or  per  accidens,  or  particularly , and  O by 
permutation  into  I and  then  simply. 

300.  In  consequence  of  the  laws  of  Conversion  we 
immediate  in-  have  from  any  Exposita,  its  converse  as  an 

ference  by  Con-  T -i . . T X 1 

version.  Immediate  Interence. 


IY.  Of  the  Substitution  of  Terms. 

301.  In  every  categorical  Affirmative  Proposition  we 
substitution  of  may  always  substitute  for  the  Predicate  any 

Predicates  in.*7  i J 

Affirmatives,  term  which  denotes  a wider  and  compre- 
hending sphere  and  the  Proposition  will  remain  true, 
but  it  will  cease  to  be  the  whole  truth.  In  the  same 
substitution  of  way  we  may  substitute  for  the  subject  any 
the  subject.  term  which  denotes  a narrower  and  compre- 
hended sphere,  and  with  the  same  effect  upon  the  Propo- 
sition it  will  still  be  true,  but  not  the  whole  truth  that 
was  contained  in  the  Proposition  before  the  change 
was  made.  Thus,  if  A B is  “ a negro,”  he  is  “ a man,” 
“ an  animal,”  “ a created  being,”  &c.  Or  if  we  say, 
“ men  are  mortal,”  we  may  say  “ Caucasians  are  mor- 
tal,” “ Americans  are  mortal,”  “ Yankees  are  mortal,” 
“ Bostonians  are  mortal,”  &c. 

302.  By  such  change  Propositions  are  said  to  be- 
come more  general  or  more  indefinite  ; they  are  true 
but  not  the  whole  truth. 

303.  In  Negative  Propositions,  in  consequence  of 
substitution  of  the  fact  that  the  Predicate  is  distributed,  we 
Negatives.-  in  may  substitute  in  the  Predicate  terms  in  the 
inverse  order  ; that  is,  for  any  comprehensive  term  we 
may  substitute  any  one  of  its  included  spheres.  Thus 
A B is  not  a man,  therefore  he  is  not  a Negro.  If 
Victoria  is  not  a sovereign  she  is  not  Queen  of  Eng- 
land. 

304.  But  we  may  not  substitute  Predicates  in  the 


n.] 


OF  PROPOSITIONS. SECT.  XI. 


77 


inverse  order  in  either  case  ; that  is,  not  a narrower 
for  a more  comprehensive  in  Affirmatives,  . no  substitutes 

x t . n ln  *he  inverse 

nor  a more  comprehensive  tor  a narrower  order, 
in  Negatives.  This  would  be  in  either  case  asserting 
something  more  than  the  truth.* 

305.  By  these  substitutions  new  Propositions  are 
made,  the  truth  of  which  depends  upon  that  immediate  in- 
ot  the  Propositions  tor  whose  terms  the  new  stitution. 
ones  are  introduced.  Hence  the  new  Propositions 
must  he  true  (though  inadequate),  by  Immediate  In- 
ference. 


SECTION  XI. 

Of  Complex  Propositions. 

306.  A Categorical  Proposition  is  called  simple 
when  its  two  terms  are  expressed  by  single  simple  and 

-r-.  , , Complex  Pro- 

WOrdS.  But  when  several  words  are  re-  positions, 
quired  to  express  the  cognition  the  term  is  called 
Complex. 

307.  It  is  evident  that  any  substantive,  or  other 
word  which  is  the  name  of  a thing,  a pro-  Necessity  for 
perty,  an  action,  or  a series  of  actions,  may  Complex  terms- 
be  a term,  as  “ man,”  “ whiteness,”  a “ step,”  “ walk- 
ing,” “ to  err.”  And  if  any  language  were  copious 
enough  to  afford  a name  for  every  possible  conception 
which  we  might  ever  wish  to  express,  as  either  the 
subject  or  the  predicate  in  our  judgments,  we  should 


* It  may  be  well  to  give  a diagram  illustrating  the  preceding  para- 
graph. 

Thus  let  S and  P he  any  two  circles  or  spheres.  S included  SfCSP 
in  P — this  represents  the  affirmative  Proposition  S is  P.  It  is  ( ( S ) ) 
manifest  that  any  sphere  comprehending  P must  comprehend  — */ 

S also.  Let  S he  Negro,  P he  Man,  and  we  have  “ Negroes 
are  Men.”  But  let  a circle  drawn  around  P denote  “ animal,”  so  that  all 
men  are  animals,  then  will  it  include  S also,  and  we  shall  have  “ Negroes 
are  animals.” 

But  in  case  of  the  Negative  Proposition  the  Subject  is  , — v 

not  included  in  the  Predicate,  and  we  have  two  circles  S and  ( S ) ( P ) 

P,  having  no  point  in  common.  S is  not  P,  consequently  S ^ ^ ^ ^ 

cannot  he  in  any  narroxver  sphere  which  is  included  in  P,  or  any  part  of  it. 


78 


LOGIC. PAHT  i. 


[CHAP. 


never  need  to  nse  any  other  words  to  express  our 
meaning  than  these  simple  terms.  But  such  is  not  the 
case  and  never  can  be  the  case  with  any  human  lan- 
guage. 

308.  In  most  cases  also  when  the  predicate  denotes 
a property  which  is  not  one  of  the  differentia  of  a spe- 
cies, we  wish  to  use  in  the  subject  not  merely  the  specific 
term  but  also  the  term  denoting  the  genus  under  which 
the  species  is  included.  Thus  if  we  say,  “ Men  who  walk 
by  faith  place  a light  estimate  upon  the  mere  vanities 
of  worldly  splendor,”  we  give  first  in  the  subject  the 
genus  “ men,”  and  then  the  species  “ who  walk  by 
faith.”  It  is  obvious  that  we  do  not  intend  to  affirm 
the  predicate  0f  the  whole  genus  denoted  by  the 
term  “ man,”  hut  only  of  one  species  of  men,  whose 
differentia  is  that  they  “ walk  by  faith.” 

309.  A simple  term,  as  “ man,”  thus  limited  be- 
Moduis.  comes  a complex  term  ; and  the  words  limit- 
ing or  qualifying  its  meaning  or  its  sphere,  are  called 
Modals. 

310.  Modals  are  either  Explicative , Differential , 
Exceptional , Exclusive , Conditional  or  Protensive. 

311.  Explicative  Modals  are  merely  rhetorical. 
Explicative^.  They  amplify  the  meaning  of  the  term 
itself,  as  when  we  say  “ mortal  man.”  Since  all  men 
are  mortal  the  adjective  adds  nothing  either  to  the 
matter  or  the  sphere  of  the  conception  for  which  the 
term  “ man  ” stands,  however  much  it  may  add  to  the 
rhetorical  effect  of  its  utterance. 

312.  Differential  Modals  limit  the  sphere  of  the 
Differential.  conception  denoted  by  the  absolute  or  sim- 
ple term.  In  that  case  the  term  is  really  the  species, 
as  the  Differential  Modal  furnishes  the  Differentia  of 
the  contained  species.  Thus  “ white  men,  ” — here 
“ men  ” is  the  simple  term,  “ white  ” the  modal ; and 
“ white  men,”  the  complex  term,  is  but  a species  of 
the  genus  a man  ” denoted  by  the  differential  “ white.” 

313.  While  Differential  Modals  indicate  the  part 
of  the  Proximate  Genus,  which  is  included  in  the  scope 


n.] 


OF  PROPOSITIONS. SECT.  XI. 


79 


of  the  judgment,  we  have  another  class  of  modals 
called  Exceptionals , which  indicate  the  part  Exceptional, 
which  is  not  included  in  the  scope  of  the  judgment. 
As  “ all  except  the  Apostles  were  scattered  abroad.” 
Instead  of  giving  the  differentia  of  that  portion  of  the 
Proximate  genus  which  is  included  in  the  Predicate, 
it  gives  the  differentia  of  the  part  which  is  not  in- 
cluded. Hence  the  Differential  and  the  Exceptional 
modals  are  in  a sense  counterparts  and  complements 
of  each  other. 

311.  The  Exclusive  Modals  are  those  which  show 
that  the  predicate  can  have  no  other  subject  Exclusive, 
than  that  of  which  it  is  predicated  in  the  judgment. 
As  “ Virtue  is  the  only  thing  worth  living  for.”  Here 
virtue  is  declared  to  be  worth  living  for.  But  by  the 
modal  every  thing  except  virtue  is  excluded  from  the 
sphere  of  the  conception  denoted  by  the  matter  “ worth 
living  for.”  Hence  of  necessity  Exclusive  modals  dis- 
tribute the  Predicate. 

315.  Conditional  Modals  express  some  separable 
mode  or  condition  of  the  object  represented  conditional, 
by  the  term,  so  that  the  object  is  included  in  the  scope 
of  the  judgment  only  while  it  is  subject  to  that  condi- 
tion. Thus  “ drowning  men  catch  at  straws  ; ” that  is, 
“ men  in  the  condition  of  drowning.”  It  does  not  ap- 
ply the  predicate  to  any  species  of  men  at  all  times 
and  under  all  conditions  as  the  Differential  modal  does, 
but  it  makes  it  applicable  to  all  men  when  they  are  in 
the  specified  condition. 

316.  Protensive  Modals  limit  the  inclusion  of  the 
term  within  the  scope  of  the  judgment  in  Protensive. 
reference  to  time.  Thus  “the  weather  is  excessively 
cold  in  winter ,” — “ our  plans  will  sometimes  fail,” — 
“ testimony  sometimes  deceives  us.” 

117.  The  Protensive  Modal  neither  makes  nor  im- 
plies any  change  in  the  properties  of  the  term,  bilt  only 
refers  to  the  time  when  the  object  denoted  by  the  term 
is  included  in  the  scope  of  the  judgment.  This  it  may 
do  definitely , as  “ in  winter ; ” or  indefinitely , as  “ some- 


LOGIC.— PAKT  I. 


80 


[chap. 


times  ; ” instantly,  as  “ now  ; ” or  absolutely , as  “ al- 
ways.” 

318.  There  is  another  kind  of  adjective  phrase  that 
has  sometimes  been  regarded  as  a modal,  which  how- 
ever I have  preferred  to  regard  as  constituting  a com- 
pound Copulative  Categoric  Proposition  (see  322), — as 
“ Hamilton , the  greatest  statesman  of  his  agef  or  “ who 
was  the  greatest  statesman ,”  &c.,  “ was  a Federalist .” 
But  the  Avords  marked  in  italics  do  not  constitute  a 
modal  of  “ Hamilton,”  they  are  the  Predicate  of  a 
judgment  to  which  “Hamilton”  is  subject,  and  the 
Proposition  expresses  the  tAvo  entirely  distinct  and  in- 
dependent judgments,  that  “Hamilton  was  the  greatest 
statesman,”  &c.,  and  that  “ he  was  a Federalist.” 

SECTION  XII. 

Of  Compound  Propositions. 

319.  Any  Proposition  which  has  more  than  two 
distinct  terms  is  called  a Compound  Proposition,  and 

compound  contains  either  expressly  or  impliedly  more 
propositions,  than  one  judgment.  If  it  has  but  tAvo  terms, 
whether  simple  or  complex,  the  Proposition  is  simple. 

320.  Compound  Propositions  are  usually  divided 
into  Express  and  Implied.  They  are  called  Express 

Express  and  when  tAvo  or  more  judgments  are  expressed 
implied.  jn  the  same  Proposition,  and  Implied  when 
one  only  is  expressed  and  the  other  is  implied. 

The  Compound  Express  Propositions  are  either 
Copulative , Causal , Discretive,  Conditional , or  Dis- 
junctive. 

321.  In  the  Copulative  Propositions  either  the  Sub- 
copuiative.  ject  or  the  Predicate,  or  both,  consist  of  two 
or  more  terms  connected  by  a conjunction.  Thus  A 
and  B are  C ; A is  B and  C ; A and  B are  C and  D. 
“ Life *and  Death  are  both  before  us;” — “Bacon  was 
both  a philosopher  and  a statesman.” 

322.  Sometimes  the  conjunction  is  omitted  entirely, 
as  “ Hamilton  the  greatest  statesman  of  his  age  was  a 


n.] 


OF  PROPOSITIONS. — SECT.  IE. 


81 


Federalist.”  And  again  its  place  is  supplied  bj  the 
relative  pronoun  and  the  verb,  as  “ Hamilton  who  was 
the  greatest  statesman,  &c.,  was  a Federalist.” 

323.  Copulative  Propositions  can  be  resolved  into 
simple  ones  according  to  the  number  of  sim-  Resolved  in 
pie  judgments  contained  in  them.  Thus  in  «™s!e  Prop°31' 
the  example,  “ Bacon  was  a philosopher  and  states- 
man,” we  have — Bacon  was  a philosopher, 

“ “ a statesman ; 

or  in  the  other  example  given,  we  have  the  following : 
Life  is  before  us, 


321.  Or  the  connective  may  be  a disjunctive  con- 
junction, as  “ Neither  wealth  nor  friends  Disjunctively 
can  free  the  body  from  its  pains,  nor  the  connected- 
mind  from  its  fears  ; ” — and  we  have, 


325.  It  is  of  course  quite  possible  that  one  of  the 
judgments  in  a compound  copulative  will  be  true,  and 
the  other  or  others  be  untrue.  And  advan- 
tage is  often  taken  of  this  fact  for  the  pur-  judgments  c»mC 
pose  of  introducing  and  gaining  assent  to  a ine  ' 
judgment  which  is  untrue,  by  ascribing  to  a subject 
two  predicates,  one  true  and  the  other  false. 

326.  Compound  Propositions  are  called  Causal  wdien 
one  of  the  judgments  assigns  the  cause  or  causal, 
sign  of  the  truth  of  the  other.  “ Christians  are  happy 
because  they  have  obtained  the  favor  of  God  ; — “ The 
evil  are  exalted  that  they  may  fall  j ” — ■“  Christ  came 
to  save  the  world  / ” that  is,  “ Christ  came  [first  judg- 
ment] that  he  might  save  the  world,”  [the  final  cause 
or  object  for  which  He  came  into  the  world.] 

327.  Compound  Propositions  are  called  Discretives 
when  they  contain  two  judgments  in  oppo-  Discretives. 
site  qualities.  Thus  “ A is  B,  but  it  is  not  D.  “ A 
and  not  B is  C.”  “ A is  B but  C is  not  D.”  “ Fortune 


Death  “ “ “ 


Friends  cannot 


Wealth  cannot 


82 


LOGIC. — PART  I. 


[CHAP. 


may  take  from  ns  our  friends  but  it  cannot  take  our 
honor.”  “ But  few  men  succeed  in  enrolling  their 
names  on  the  list  of  those  who  are  never  to  be  forgot- 
ten ; ” that  is,  “ some  men  do  and  some  do  not  suc- 
ceed,” &c. 

328.  We  have  already  seen  that  Conditional  and 
Disjunctive  Propositions  are  compounded,  implying 
first  categorical  judgments  and  then  a hypothetical 
relation  between  those  judgments.  Hence  in  one  point 
of  view  they  are  to  be  regarded  as  compounds  of  cate- 
gorical judgments. 

329.  In  the  compound  of  the  categorical  with  the 
conditional.  conditional,  the  conditional  clause  is  to  be 
regarded  as  a modal.  Thus  if  A is  B,  C is  D ; that  is, 
C is  D ( sub  modo ) A is  B.  “ If  the  Scriptures  come  from 
God  they  are  entitled  to  the  highest  respect.”— “ The 
Scriptures  are  entitled  to  the  highest  respect  on  con- 
dition [conditional  modal]  that  they  come  from 
God.” 

330.  So  with  the  Disjunctive,  A is  either  B or  C. 
Disjunctive.  A is  B on  condition  that  it  is  not  C,  or 
either  A or  B is  C ; that  is,  A is  C on  condition  that  B 
is  not.  “ The  author  of  this  statement  is  either  a fool 
or  a knave.”  He  is  a knave  on  condition  he  is  not  fool 
enough  not  to  know  better. 

331.  The  more  usual  form,  however,  of  the  com- 
pound categorical  with  one  disjunctive  term,  is  that  in 
which  one  term  denotes  a logical  whole,  and  the  other 
the  parts  ; as  “ All  men  are  either  Caucasian,  Mongol, 
or  Negro.” 

We  shall  of  course  reserve  the  consideration  of  the 
judgments  which  connect  the  Conditional  and  Disjunc- 
tive members  of  these  compounds  until  a subsequent 
place  in  our  treatise. 

832.  Of  the  Compound  Implied  Propositions  two 
only  need  to  be  mentioned,  the  Executives  and  the 
Exclusives.  They  each  imply  a judgment  different  in 
quality  from  the  one  expressed — this  is  done  by  a 
modal. 


II.] 


OF  PROPOSITIONS. SECT.  XII. 


83 


333.  Thus  Exceptives  while  including  the  expressed 
subject  in  the  sphere  of  the  predicate,  make  an  excep- 
tion of  some  of  the  individuals  included  in  Exceptives. 
the  implied  subject,  which  consequently  are  excluded 
from  it.  Thus  “ All  but  the  Apostles  fled”  implies 
that  there  were  some  who  were  not  Apostles  that  did 
flee. 

334.  In  this  case  the  expressed  judgment  is  affirma- 
tive and  the  implied  is  negative.  But  if  we  say, 
“ None  but  the  Apostles  remained ,”  we  have  the  nega- 
tive judgment  expressed,  “None ; ” that  is,  “ no  Chris- 
tians remained,” — and  the  implied  affirmative  judg- 
ment, “ the  Apostles  did  remain.” 

335.  The  Exclusive  Propositions,  while  including  a 
subject  in  any  predicate,  exclude  by  an  im-  Exdusivos. 
plied  negative  judgment  all  other  subjects  from  that 
predicate,  as  “ Virtue  is  the  only  thing  worth  living 
for.”  This  is  precisely  the  same  as  the  Exceptive  in 
which  the  negative  judgment  is  expressed,  as  “Nothing 
but  virtue  is  worth  living  for.” 

336.  The  article  “the”  before  the  Predicate  of  an 
Affirmative  judgment  constitutes  it  an  Exclusive,  by 
making  the  Predicate  a definite  and  distributed  term. 
Thus  “ Christ  is  the  Saviour  of  the  world  ; ” this  im- 
plies that  He  is  the  only  Saviour. 

337.  In  the  conversion  of  complex  and  compound 
Propositions  they  must,  as  a general  thing,  be  first  re- 
solved into  simple  incomplex  propositions,  and  per- 
muted and  converted  according  to  the  rules  already 
laid  down.  In  one  or  two  cases,  however,  there  are 
facts  in  regard  to  their  conversion  worth  noticing. 

338.  Exceptionals  and  Exclusives  are  easily  con- 
verted into  each  other.  “ All  but  the  Apostles  fled  ; ” 
becomes  by  substituting  the  exclusive  instead  Exreptionals 
of  the  exceptional  modal,  and  changing  the  and  'Exclusives 
quality  of  the  Proposition,  “ The  Apostles  convertlble- 
alone  did  not  flee.”  The  same  thing  would  be  accom- 
plished with  the  antithetic  Predicate  without  changing 
the  qualify  of  the  copula,  as  the  Apostles  alone  re^ 


84 


LOGIC. PART  I. 


[CHAP. 


mained,  i.  e.,  did  not  flee.  “ Virtue  is  the  only  thing 
worth  living  for,”  is  converted  into  an  exceptional  by 
substituting  for  the  subject  “nothing,”  and  the  ex- 
ceptional modal  before  the  subject,  as  “ Nothing  except 
virtue  is  worth  living  for.” 

339.  Any  Compound  Proposition,  whether  Express 
or  Implied,  may  always  be  regarded  for  the  purposes 

compound  of  Deduction  as  a simple  Complex  Proposi- 
ducFble  tocom!  tioii . Thus  the  Copulative  “ A and  B are  C.” 
plex-  A (sub  modo,  that  is,  on  condition  it  is  joined 

to  B)  is  C.  For  the  Causal  take  “ A is  B because  it  is  C.” 
A ( sub  modo , that  is,  because  it  is  C)  is  B.  For  the 
Discretive  “ A is  B but  not  C.”  A (sub  modo , that  is, 
on  condition  it  is  not  C)  is  B.  The  same  is  obvious, 
too,  with  regard  to  the  Exclusives  and  Exceptional  ; 
the  exclusive  and  exceptional  phrases  may  be  made  or 
regarded  as  merely  a modal  of  one  of  the  terms. 

340.  But  we  may  carry  this  matter  one  step  further, 
and  regard  the  Complex  as  a Simple  Categorical  so  far 

complex  to  as  the  purposes  of  deduction  are  concerned, 
simple.  ]y  depends  very  much  upon  the  fulness  of  a 
language,  whether  a conception  shall  be  expressed  by 
a single  term  or  not.  If  we  have  no  single  term  for  it, 
we  must  use  several,  and  give  either  its  description  or 
its  definition  instead  of  the  term  itself.  And  all  the 
words  which  Logic  requires  in  the  expression  of  judg- 
ments, are  either  the  copula  or  the  terms  ; or  instead 
of  terms,  their  definitions  or  descriptions.  Hence  what- 
ever words  are  necessary  to  express  any  cognition, 
become  but  a complex  term  for  that  cognition,  and  it 
is  merely  accidental  for  all  logical  purposes,  whether  a 
term  be  expressed  by  one  word  or  by  many. 

SECTION  XIII. 

Of  Comparative  Judgments. 

341.  Comparative  Judgments  do  not  include  the 
subject  in  the  sphere  of  the  Predicate. 


n.]  OF  PROPOSITIONS. SECT.  XIII.  85 

342.  In  Comparisons  tliere  are  three  terms  and  two 
implied  categorical  judgments  : as  “ A is  Three  Terms 

. x , t?  TT  ^ ° in  Comparative 

wiser  than  ±5.  Here  we  mamiestly  have  Judgments, 

the  two  judgments,  A is  wise  and  B is  wiser.  And  we 
have  three  terms,  A the  Subject,  B the  Predicate,  and 
the  Comparative  term,  which  in  this  case  is  “ wise.” 
The  Predicate  is  assumed  as  the  Standard  ^The^posUive 
or  Positive  term,  and  the  Subject  is  com-  pared  Terms'11 
pared  with  it  and  is  the  Compared  term. 

343.  Of  Comparative  Judgments  there  may  be 
reckoned  seven  kinds:  1.  Comparatives  of  Different  kinds 
simple  Intensity.  2.  Comparatives  of  Inten-  °f  comparatives 
sity  considered  as  a Cause.  3.  Comparatives  of  Time. 
4.  Of  Place.  5.  Of  Manner.  6.  Of  Means  or  Method. 
1.  Of  Ratio  or  Relation. 

344.  We  may  have  comparisons  in  Intensity  of 
three  varieties  : (1)  of  Equality  ; (2)  the  Indefinite  ; 
(3)  Comparisons  of  Inequality. 

(1.)  In  Comparisons  of  Equality  the  Positive  and 
Compared  terms  are  affirmed  to  be  equal  in  comparisons 
the  intensity  of  the  term  of  Comparison ; of&iuality- 
as  A is  equal  to  B,  in  which  it  is  also  implied  that 
B is  equal  to  A,  or  that  A and  B are  equal  in  the 
intensity  of  that  in  respect  to  which  they  are  com- 
pared. 

(2.)  In  the  Indefinite  we  have  the  Compared  term 
declared  to  he  of  as  great  an  intensity  as  the  indefinite. 
Positive ; as  “A  is  as  great  as  B,”  or  “ A is  as  wise 
as  B.”  In  these  judgments  it  does  not  appear  that  B 
is  not  wiser  than  A,  &c. 

(3.)  In  Comparatives  of  Inequality  the  term  of  com- 
parison is  used  in  the  comparative  degree,  inequality, 
and  a difference  in  degree  of  intensity  is  declared  to 
exist  between  the  Positive  and  the  Compared  terms  ; 
thus  A is  greater  than  B,  or  A is  less  than  B. 

345.  Comparatives  of  Inequality  differ  in  their  in- 
tensity, by  being  on  the  different  sides  of  the  Difference  of 
positive  degree,  and  are  accordingly  called  Intensity- 
comparisons  of  greater  or  of  less  intensity. 


86 


LOGIC. PAKT  I. 


[CHAP. 


sity 


346.  Comparisons  are  said  to  be  of  greater  intensity 
Greater  mten-  when  the  Term  of  Comparison  is  affirmed  to 

belong  to  the  Compared  in  greater  intensity 
than  to  the  Positive,  and  Comparisons  of  less  inten- 
Less  intensity,  sity  when  the  Term  of  Comparison  is  affirmed 
of  the  Compared  in  a less  intensity.  Thus  A is  greater 
than  B,  is  a comparison  of  greater  intensity — A is  less 
than  B,  is  one  of  less  intensity. 

347.  We  may  have  Comparatives  in  which  the  in- 
intensity  as  a tensity  of  the  comparative  term  is  considered 

Cause-  as  a Cause.  Thus,  “ The  weather  is  so  cold 
that  the  water  freezes.” 

348.  For  a comparison  of  Time  we  say  that  “ A 

of -rime.  occurs  when  B occurs;”  as  “It  lightens 

when  it  thunders.” 

349.  For  a comparison  in  Place  we  say,  “A  is  where 
of  piace.  B is.” — “ Where  two  or  three  are 
together  in  My  name,  there  am  I in  their  midst.” 

350.  For  a comparison  of  Manner  we  say,  “ A is 
of  Manner.  like  B.” — “ The  Boy  walks  like  his  Father.” 

351.  We  have  also  a comparative  of  Method  or 
of  Method  and  Means,  as  “He  came  as  he  went ; ” in  which 

case  the  “ as  ” comparative  may  refer  to 
either  the  means  used  or  to  the  way  by  which  the  act 
was  performed. 

352.  Then  we  have  Ratios,  or  comparisons  of  value, 
of  Ratio.  in  which  one  term  varies  as  the  other.  Thus 
“ A is  to  B as  C is  to  D. — “ The  Mercury  in  the  Ther- 
mometer rises  and  falls  as  the  weather  grows  warmer 
or  colder.” 

353.  In  comjiarisons  of  Inequality  conversion  may 
Conversion  of  be  effected  by  change  of  the  intensity  to  its 

comparatives.  0pp0gjf-e.  Thus  “ A is  greater  than  B,” — 
“ B is  less  than  A.” 

354.  But  in  the  Indefinite  no  conversion  can  be 

as  great  as  B.” 


gathered 


Indefinites  can- 
not be  convert- 
ed. 


effected ; we  say,  “A  is 


But  the  judgment  leaves  it  possible  for  A to 
be  greater  than  B,  and  the  mind  is  uncertain  whether 
it  is  or  not.  Hence  B may  be  either  equal  to  A,  or  less 


II.] 


OF  PROPOSITIONS. SECT.  XIV. 


87 


than  A ; and  the  judgment  does  not  furnish  the  means 
for  determining  which  it  is. 

355.  Comparatives  in  which  the  Intensity  is  re- 

garded  as  a Cause,  are  converted  into  Causal  comparatives 
htegoric  Propositions.  “ It  is  so  cold  that  caS!Ld  ‘"t" 
the  water  freezes,”  becomes  “ the  water  freezes  because 
it  [the  weather]  is  so  cold.” 

356.  All  the  other  forms  may  be  regarded  as  Com- 
paratives of  Equality  so  far  as  conversion  is  concerned, 
and  as  such  may  be  converted  simply,  A is  equal  to  B, 
therefore  B is  equal  to  A. 

SECTION  XIV. 

Of  Probable  Judgments. 

357.  A Problematical  Judgment  is  one  in  which  it 
is  affirmed  that  the  Copula  may  be  affirmative.  Probable  Judg_ 
But  a Probable  Judgment  is  one  in  .which  ments- 
there  is  given  an  estimate  of  the  reasons  for  affirming 
the  Copula. 

358.  The  value  of  the  Probability  is  always  esti- 
mated (if  at  all)  in  a fraction  of  unity  or  in  a Their  value, 
ratio ; unity  being  assumed  as  the  same  as  a cer- 
tainty. 

359.  The  value  is  ascertained  by  a calculation  of 
chances.  One  reason  for  believing  any  Pro-  How  ascer. 
position  which  comes  into  the  present  class  tained- 
to  be  true,  is  because  we  have  known  it,  or  some- 
thing like  it  to  hold  true.  Thus  of  any  given  side  of  a 
die  there  is  a probability  that  it  will  fall  uppermost 
at  any  given  throw.  If  a man  commits  a crime  there 
is  a probability  that  he  will  be  detected,  based  indeed 
upon  the  means  used  for  his  detection ; but  estimated 
by  the  proportion  which  the  times  in  which  similar 
means  have  been  successful  in  similar  cases  bear  to  the 
times  in  which  they  have  failed. 

360.  All  the  known  cases  are  considered  as  so 
many  Chances , which  are  divided  into  two  chances  favor, 
classes — the  favorable  and  the  unfavorable  ; onibiend  u"fav" 


88 


LOGIC. PART  I. 


[CHAP. 


and  the  probability  of  any  affirmative  judgment  hav- 
ing an  individual  case  for  its  subject,  and  the  term  in- 
cluding the  favorable  cases  for  its  Predicate  being  true, 
is  determined  by  the  proportion  which  the  favorable 
chances  bear  to  the  unfavorable.  Thus  a die  has  six 
sides — at  one  throw  therefore  one  of  the  six  sides  must 
come  up : call  that  the  favorable  chance,  and  as  there 
are  five  other  sides,  no  one  of  which  will  be  up  when 
that  specific  one  is  uppermost,  we  may  call  the  unfa- 
vorable chances  five.  The  probability,  therefore,  of  any 
particular  side,  say  the  ace , being  up,  is  one  to  five, 
or  one-sixth  of  the  whole  number. 

361.  In  order  to  estimate  the  probability  of  any 
judgment  therefore,  we  must  have  a totality  of  cases. 
This  may  be  the  absolute  totality  including  all  actual 
and  all  possible  cases  of  the  same  kind,  or  it  may  be  any 

part  of  that  totality  which  has  fallen  under 
assumed  total-  our  observation,  assumed  as  the  representa- 
tive of  the  whole.  For  the  estimation  of  the 
probability,  it  makes  no  difference  which  is  assumed, 
provided  the  part  taken  be  an  exact  representative  of 
the  whole.  Thus  suppose  the  whole  to  be  one  thou- 
sand, out  of  which  one  hundred  have  been  favorable 
and  nine  hundred  unfavorable,  the  chances  are  one  to 
nine.  How  if  we  take  any  part  of  this  totality,  say 
one  hundred,  if  it  be  an  exact  representative  of  the 
totality,  the  chances  will  be  ten  to  ninety — that  is,  one 
to  nine  ; or  if  we  take  ten,  they  will  be  one  to  nine  still 
as  before. 

362.  The  improbability,  which  is  the  probability 
improbability,  that  the  individual  will  be  included  among 
the  unfavorable  chances,  is  of  course  the  complement 
of  the  probability  in  the  unity  of  the  whole,  whether 
absolute  or  assumed.  Thus  if  the  Probability  is  three- 
fourths,  the  Improbability  is  one-fourth. 

363.  The  balance  of  Probabilities  is  the  difference 
Balance  of  pro-  between  the  two  fractions,  and  is  in  favor 
buiities.  0f  the  probability  or  the  improbability,  as 
the  one  or  the  other  happens  to  be  the  largest. 


n.] 


OF  PROPOSITIONS. — SECT.  XIV. 


89 


364.  The  Improbability  is  not  however  the  same  as 
the  Probability  of  the  opposite.  Thus,  in  lmprobability 
throwing  a penny,  the  probability  of  the  not  the  same  as 
head  side  falling  up  is  I,  the  probability  of  the  opposite  re- 
its  falling  up  in  two  throws  is,  say  f,  conse- 
quently the  improbability  is  f . But  the  probability  that 
the  head  will  fall  down,  or  the  tail  fall  up,  one  in  two, 
is  also  f instead  of  p 

365.  Both  the  Probability  and  the  Improbability 
are  sometimes  called  Antecedent  Probability  Antecedent 
and  Antecedent  Improbability,  with  reference  Probability, 
to  the  fact  that  they  are  estimated  before  or  antecedent 
to  the  special  reasons  for  affirming  the  judgment  in  any 
given  case.  Thus  the  antecedent  improbability  of  a 
miracle  is  based  upon  the  uniformity  of  nature  ; that  is, 
the  numberless  instances  in  which  no  mira-  Effectof  differ- 
cle  has  been  wrought.  On  the  other  hand,  ent  totam“^ 
it  has  been  claimed  that  when  we  consider  the  special 
occasion  on  which  it  is  claimed  that  miracles  have 
been  wrought,  there  is  an  antecedent  probability  in 
their  favor ; the  difference  in  the  estimates  arises  from 
the  assumption  of  different  totalities  of  cases  or  chances. 
In  the  one  case,  forgetting  the  special  occasion  or  pur- 
pose,* the  absolute  totality  of  histoi’ic  events  and  of 
occurrences  in  nature  is  assumed.  In  the  other  it  is 
assumed  that  the  object  for  which  the  miracle  is  al- 
leged to  have  been  wrought,  is  to  constitute  the  basis 
of  an  entirely  different  totality,  is  the  Differentia  of  a 
much  narrower  sphere,  within  which  the  chances  are 
not  only  much  fewer,  but  are  such  as  to  turn  the 
balance  of  the  probabilities  on  to  the  other  side. 

366.  In  many  cases  this  value  can  be  expressed  with 
as  much  certainty  as  any  categorical  judgment  what- 
ever. But  there  are  also  some  objects  both  Exact  estimate 
in  logical  and  in  comparative  quantity,  ofvalue- 
whose  quantity  cannot  be  expressed  in  terms  of  dis- 
crete quantity  at  all. 


* Nodus  deo  dignus. 


90 


LOGIC. — PART  I. 


[chap. 


367.  In  most  cases,  however,  our  estimate  of  the  value 
of  a probability  cau  be  only  approximate.  "We  judge 
Approximate  as  nearly  as  we  can  from  what  lias  fallen 
estimate.  under  our  experience,  assumed  as  a repre- 
sentative of  the  whole,  the  proportion  of  the  favorable 
cases  to  the  unfavorable  in  the  absolute  whole. 


368.  The  probability  against  any  judgment  or  Pro- 
!m’brot)'1hTtand  Positi°n  is  called  its  improbability ; and  the 
mail™ unity. y probability  and  the  improbability  together 
make  up  a unit  or  certainty. 

369.  Hence  if  we  have  either  the  Probability  or  the 
Improbability  given  in  a fraction  or  a ratio,  we  can 
find  the  other  by  subtracting  the  fraction  from  unity, 
or  by  converting  the  ratio. 

370.  But  while  the  improbability  can  never  be 
mamprbeabliess  more  ^ian  the  complement  of  the  probability 
than  the  com-  in  the  unity  of  the  logical  whole,  it  may  often 

plement  of  the  J ° J 

Probability.  be  leSS. 

371.  It  will  happen  in  many  cases  that  we  know 
illustration.  of  many  reasons  for  believing  a proposition, 
and  none  for  disbelieving ; that  is,  we  may  know  many 
favorable  chances  and  be  entirely  ignorant  whether 
there  are  really  any  unfavorable  ones  or  not.  Thus  in 
the  moral  government  of  God,  it  is  perfectly  certain 
that  in  many  cases  sins  are  punished  in  this  world, 
and  perhaps  it  is  not  certain  that  there  is  any  case  in 
which  they  are  not  punished  in  this  world.  Hence 
there  is  on  the  supposition  a strong  probability  in  favor 
of  the  opinion,  that  any  particular  sin  will  be  punished 
in  this  world  and  none  whatever  against  it. 

372.  Improbability,  therefore,  is  not  the  mere  want 
improbability  or  absence  of  probability  or  grounds  for  be- 

of  Probability,  lieviug.  But  it  is  something  positive.  It  is 
based  upon  and  therefore  implies  positive  ground  for 
(Zwbelieving,  or  believing  the  contradictory  of  a pro- 
position. 

373.  There  may  also  be  an  improbability  against  a 
proposition,  when  there  is  no  probability  or  nothing  in 
its  favor ; and  for  the  same  reasons  as  we  have  just 


n.] 


OF  PROPOSITIONS. SECT.  XV. 


91 


given  for  there  being  in  some  cases  a probability  with- 
out any  counter  improbability. 

371.  There  may  be  many  cases  in  which  the  general 
probability  of  which  we  have  just  been  speak-  Generaj^and 
ing,  may  be  increased  or  diminished  by  spe-  bmties. 
cial  grounds.  Thus,  in  a community  where  one  in  ten 
die  of  any  special  disease,  the  probability  that  any 
particular  individual  would  die  with  that  disease  is 
increased  or  diminished  by  the  peculiarities  of  his 
constitution,  mode  of  life,  &c.  The  rates  of  life  insur- 
ance are  lived  upon  the  general  probability  of  the 
duration  of  life.  But  this  probability  becomes  so  much 
diminished  by  one’s  being  sick  or  constitutionally  dis- 
eased, that  Life  Insurance  Societies  refuse  insurance  in 
such  cases.  In  Marine  and  Fire  Insurances  also,  the 
rate  of  insurance  is  increased  above  the  general  rates 
by  considerations  affecting  the  probability  of  loss,  aris- 
ing from  the  special  circumstances  of  the  property 
insured. 


SECTION  XY. 

Of  Conditional  Judgments. 

375.  Conditional  Judgments  affirm  the  reality  of 
the  Predicate,  on  the  ground  of  the  reality  of  conditional 
the  Subject.  But  as  the  Subject  and  Predi-  Judsmf=nts. 
cate  are  not  cognitions  merely  but  rather  judgments, 
of  which  the  copula  of  the  second  is  affirmed  on  the 
ground  of  the  copula  of  the  first,  the  first  judgment 
is  called  the  Antecedent , and  the  second  Antecedent  and 
the  Consequent / thus  “If  A is  B,  C is  D.”  Conse<iuent- 
Here  “ A is  B ” is  Antecedent — “ C is  D ” is  Consequent. 

376.  The  Antecedent  and  Consequent  taken  toge- 

ther are  called  the  Members  of  the  Condi-  Members  o. 
tional ; they  are  also  its  Matter.  concution«i.the 

377.  In  all  Conditional  Judgments  there  must  be 
at  least  three  terms  and  two  copulas,  as  in  Three  Termg 
the  case  just  given.  There  may  also  be  four  atleast- 
terms,  as  “If  A is  B,  C is  D.”  “If  each  man  may 


92 


LOGIC. PART  I. 


[chap. 


hold  what  opinion  he  chooses  without  blame,  atheism 
itself  will  he  innocent.”  Here  we  have  the  four  dis- 
tinct terms,  “ each  man,”  “ hold  what  opinion  he 
chooses,”  “ atheism,”  and  “ innocent.” 

378.  The  ground  of  affirmation  in  Conditional  Judg- 
sequence.  meuts  is  called  the  Sequence.  Thus  if  we 
have,  “ If  A is  B,  C is  D,”  we  may  ask  why  ? On 
what  grounds  can  we  affirm  the  judgment,  “ C is  D,” 
as  a consequent  of  the  judgment  that  “ A is  B ? ”- — the 
answer  to  this  question  is  what  is  called  the  Sequence. 

379.  For  the  most  part  the  sequence  or  ground  of 
affirmation  is  self-evident ; and  for  this  reason  it  has 

Not  always  seldom  received  much  attention.  But  we 
self-evident.  may  have  a conditional  judgment  when  there 
is  really  no  sequence  ; thus  the  gardener  says,  that 
“ If  he  plants  any  onions  in  the  new  of  the  moon,  they 
will  fail  to  have  large  bottoms  ;”  the  judgment  is  in 
form  a conditional.  But  still  one  may  fail  to  see  any 
connection  between  its  members. 

380.  It  becomes  necessary,  therefore,  to  consider 
sequence  can  the  grounds  of  affirmation  in  the  Sequence. 

ed  as  a cate-  Ibis  can  oi  course  always  be  stated,  as  a 
mental  Jude'  Categorical  Proposition.  If  one  says,  “ 
John  has  a fever  he  is  sick,”  and  we  ask  why  ?- 

“ Because  all  who  have  fevers 


If 

-the 


appropriate  answer  is, 
are  sick.£. 

381.  Any  Proposition  may  be  an  Antecedent  upon 
which  any  Immediate  Inference — whether  by  (1)  Op- 
immediate  in-  position  of  Judgments,  or  (2)  by  Contra- 
ference.  position,  or  (3)  Conversion,  or  (4)  Substitu- 
tion— may  be  affirmed  as  a Consequent,  in  accordance 
with  laws  and  principles  of  Immediate  Inference  al- 
ready explained. 

382.  If  the  unlike  terms  are  mere  synonymes  or 
even  equipollent,  there  can  hardly  be  said  to  be  any 
identity  of  An-  sequence,  and  yet  the  Conditional  is  good, 
tecedents.  Thus  “ If  common  salt  is  good  for  seasoning 
food,  chloride  of  sodium  is  good  for  seasoning  food  ; ” 
the  sequence  in  this  case  is  identity  of  Antecedents. 


n.] 


OF  PKOPOSITIONS. SECT.  XV. 


93 


383.  If  tlie  Subject  is  the  same  in  both  Members, 
the  Predicate  of  the  Consequent  may  be  a 
superior  sphere,  comprehending  the  Jrredi-  the  consequent 
cate  of  the  Antecedent ; and  for  the  same  KfcAn- 
reason,  if  the  Predicate  is  the  same  in  both 
Members,  the  Subject  of  the  Consequent  may  be  any 
inferior  sphere  comprehended  in  the  sphere  of  the  Sub- 
ject of  Antecedent.  Thus  as  an  example  of 
the  first  case,  “ If  the  English  are  Anglo-  scoifsetquetnhte 
Saxons,  they  are  Caucasians.”  Here  “ An-  m'XaPo'n'ho 
glo-feaxons  are  assumed  as  but  a species 
of  “ Caucasians.”  As  an  example  of  the  second  take 
the  following : “ If  virtue  is  expedient,  temperance 
is  expedient ; ” — “ temperance  ” being  one  species  of 
“ virtue,”  or  one  of  the  virtues.  But  in  the  first  case, 
if  the  Antecedent  is  negative,  the  Predicate  of  the 
Consequent  may  be  any  narrower  sphere  predicated 
negatively  ; — ■“  If  the  English  are  not  Caucasians  they 
are  not  Anglo-Saxons.” 

38-1.  If  the  Predicate  of  the  Antecedent  be  one  of 
two  or  more  Correlatives  inhering  in  the  >Vhen  the  p,e- 
same  subject,  the  Predicate  of  the  Conse-  riStwsesarfnCthe 
quent  may  be  any  other  of  these  Correia-  saioe  object 
tives.  Thus,  “ If  an  ultimate  particle  of  matter  has 
extension,  it  has  divisibility.”  But  if  the  Correlatives 
do  not  inhere  in  the  same  object,  they  must  correlatives  in 
be  predicated  negatively  in  one  of  the  mem-  Ssibl°piedr 
bers  ; thus  “ If  the  man  is  the  master  he  is  fyat^donlgMemi 
not  the  servant.”  Or  in  general,  if  one  of  ber- 
any  two  Antithetic  terms  be  predicated  of  any  subject 
in  the  Antecedent,  the  other  may  be  predicated  of  it 
negatively  in  the  Consequent,  and  vice  verm. 

385.  The  Cause  of  any  thing  is  always  in  some 
sense  the  ground  of  its  reality.  Under  this  general 
principle  we  may  have  the  following  classes  of  Condi- 
tional Judgments  with  Antecedents  expressive  of  the 
Cause  of  the  Consequent. 

386.  Hence  if  of  several  contrary  terms,  having- 
analogous  spheres,  some  property  be  predicated  in  the 


94 


LOGIC.— PART  I. 


[chap. 


Of  opposite 
Subjects  the 
Material  Cause 
may  be  predi- 
cated in  both 
Members. 

U 


Antecedent,  which  is  of  the  essence  of  the  proximate 
genus — that  is,  the  Material  Cause — the  same  term 
may  be  predicated  of  any  contrary  term  in 
the  Consequent,  whether  that  term  be  a co- 
ordinate or  the  subordinate  of  any  coordi- 
nate to  the  subject  of  the  Antecedent.  Thus, 
If  vice  is  voluntary , virtue  is  voluntary ; ” — here 
voluntariness  of  action  is  assumed  as  the  Essentia  or 
Material  Cause  of  Moral  actions,  and  vice  and  virtue 
are  two  coordinate  species  of  Moral  actions,  each  hav- 
ing a Differentia  or  Formal  Cause  of  its  own.  And 
we  may  also  have,  “ If  vice  is  voluntary,  temperance 
[one  of  the  virtues]  is  voluntary.” 

387.  If  the  Antecedent  affirms  the  conjunction  of  the 
Efficient  and  Occasional  Causes,  the  reality 
of  the  Effect  may  be  affirmed  in  the  Conse- 
quent ; thus,  “ If  the  spark  falls  upon  the 
powder  it  will  explode,  or  an  explosion  will 
ensue.”- — If  the  boy  takes  cold  he  will  be 


Of  the  conjunc- 
tion of  the  Effi- 
cient and  Occa- 
sional Causes  in 
the  Antecedent, 
the  Effect  may 
be  affirmed  in 
the  Consequent. 

sick.” 

388 

ofthe  Material  cedent,  the  substance  or 
tecedent  the  E?"  affirmed  in  the  Consequent. 


feet  or 
quent  may 
affirmed. 


If  the  Material  Cause  is  affirmed  in  the  Ante- 

3iiu s may  be 
Thus,  “ If  ex- 
■“  If  the  mode- 
rate indulgence  of  pleasures  is  right,  the 
temperate  use  of  alcoholic  drinks  is  right.” 

389.  If  a Formal  Cause  be  affirmed  in  the  Antece- 
or the  Formal  dent  the  Consequent  may  affirm  the  species. 

Antecedent, the  Thus,  “ If  the  temperate  use  of  alcoholic 
affirmed "inhhe  stimulants  be  in  accordance  with  the  law  of 
consequent  temperance  and  self-denial,  it  is  right.” 

390.  In  cases  where  the  Conditional  has  four  dis- 
compiex  se-  tinct  terms,  the  sequence  becomes  complex 

or  double.  In  this  case  we  may  have  several 
grounds  of  affirming  the  Consequent. 

391.  When  the  Subject  of  the  Antecedent  is  re- 
substance  and  garded  as  the  Cause  of  the  Subject  of  the 


Consbee  tension  exists  matter  exists.1 
indulgence 


Mode  in  the  An 
tec 
of 
ani 

Consequent 


fecedemcauses  Consequent,  and  the  Predicate  of  the  Ante- 
and  Mode  in  the  cedent  affirms  of  its  Subject  some  mode  which 


n.] 


OF  PROPOSITIONS. SECT.  XY. 


95 


is  regarded  as  the  Cause  of  the  mode  of  the  Subject  of 
the  Consequent,  it  may  be  predicated  of  that  Subject  in 
the  Consequent.  Thus,  “ If  the  Moon  is  full  the  tides 
will  be  high.”  Here  the  Moon  is  regarded  as  the 
cause  of  the  tides,  and  the  “ fulness  ” of  the  Moon  as 
the  cause  of  the  “ highness  ” of  the  tides. 

392.  Again  the  Subject  of  the  Antecedent  may  in- 
clude the  Subject  of  the  Consequent,  and  the  subject  of  An- 
Predicate  of  th'e  Consequent  include  that 

of  the  Antecedent.  Thus,  “ If  the  English  °Lmea£dontshe 
belong  to  the  Teutonic  branch  of  the  human  conieq‘nt°come- 
family,  the  Puritans  must  be  Caucasians.”  SF^™Anntece- 
Here  “Puritans,”  Subject  of  the  Conse-  dent- 
quent,  are  regarded  as  part  of  “ the  English,”  the  Sub- 
ject of  the  Antecedent — and  “Teutons,”  the  Predicate 
of  the  Antecedent  is  included  in  Caucasians,  the  Pre- 
dicate of  the  Consequent. 

393.  Or  again  we  may  have  the  Subjects  of  both 

Members  contraries  to  each  other  regarded  subjects  in  both 
as  Formal  Causes,  and  in  that  case  the  Pre-  j°"; 

dicates  will  be  contraries  to  each  other  also  ; malCauses- 

“ If  vice  produces  misery,  virtue  may  be  expected  to 
produce  happiness.” 

394.  Or  we  may  invert  the  order  and  say,  “ If  hap- 

piness results  from  virtue,  misery  will  result  And  the  re. 
from  vice.”  verse- 

395.  But  besides  this  the  Effect  though  in  no  sense 
the  ground  of  the  reality  of  the  Cause,  is  of-  0f  the  Effect 
ten  the  sign  or  ground  of  our  knowledge  of  “ntatheArneaiity 
the  reality  of  the  Cause,  and  for  that  reason  conhse<£m  mw 
becomes  an  Antecedent,  upon  which  we  may  be  affirmed- 
always  affirm  the  reality  of  the  Cause.  If  the  Cause 
be  Immanent  or  Permanent  the  Antecedent  immanentand 
may  be  affirmed  in  the  present  tense  or  with- 

out  regard  to  protension.  But  if  it  be  only  ^nt  Ten»e.Pre' 
a Transient  Cause,  as  most  occasional  causes  Transient  only 
are,  its  reality  can  be  affirmed  in  the  Conse-  inthePast- 
quent  only  in  the  past  tense.  Thus,  “ If  there  is  day- 
light we  may  say  that  the  sun  shines  ; ” — but  “ If  there 


96 


LOGIC. PART  I. 


[chap. 


is  an  explosion,  we  may  say  that  there  has  been  powder 
and  fire.”— “ If  there  is  small  pox,  we  may  say  that 
the  infecting  virus  has  been  communicated  to  the  sys- 
tem.” 

396.  I have  said  nothing  thus  far  of  the  Quantity  of 
Quantity  anti  the  Members  of  the  Conditional.  But  as  the 
Members.  ° Antecedent  is  the  ground  on  which  we  affirm 
the  Consequent,  it  is  evident  that  no  term  which  has 
not  been  used  as  a distributed  term  in  the  Antecedent, 
may  be  used  as  a distributed  term  in  the  Consequent. 
But  for  the  most  part  terms  are  regarded  as  Continuous 
Wholes  in  Conditional  Judgments. 

397.  W e have  also  spoken  only  of  simple  Catego- 
compiex  and  ricals  as  Members  of  the  Conditional.  -But 

Membepr°un  in  these  Members  may  be  either  Complex  or 

Conditionals.  t/^j  • i i 

Compound  Uategoricals ; and  as  we  nave 
before  seen  the  Compound  may  be  regarded  as  Com- 
plex, and  the  Complex  as  simple  Categoricals — only 
taking  care  not  to  separate  or  omit  any  of  the  parts  of 
the  Complex  term. 

Besides  the  above  modes  of  compounding  the 
Conditional,  there  are  two  others  which  deserve  a 
mention. 

398.  If  we  have  two  or  more  Antecedents,  the  Co- 
pulas of  which  are  each  independent  of  the  Copulas  of 

compound  the  others  respectively,  and  one  Consequent, 
conditionals.  pqe  (]0pUia  0f  which  is  affirmed  on  condition 
of  the  truth  of  all  the  Antecedents,  we  shall  have  what 
may  be  called  a Compound  Conditional ; thus, 

If  A is  B ) A - -n. 
and  If  A is  C j 1S  ’ 

“ If  the  Departed  are  cognizant  of  what  takes  place  on 
earth,  and  if  they  retain  the  same  feelings  towards  us 
as  they  had  while  they  were  here,  they  must  sometimes 
be  intensely  pained  by  what  they  see  in  the  course  of 
life  which  we  are  now  pursuing.” 

399.  Again  we  may  have  what  is  called  a Con- 
continuous  tinuous  Conditional  in  which  the  Consequent 
conditionals.  0f  t}ie  qrst  becomes  the  Antecedent  to  the 


XI.] 


OF  PROPOSITIONS. SECT.  XVI. 


97 


second,  and  so  on.  Thus,  “ If  A is  B,  A is  C.  If  A is 
0,  A is  D,”  &c. — “ If  God  is  just  He  will  punish  the 
wicked.  And  if  He  punishes  the  wicked,  surely  they 
that  blaspheme  His  Name  will  be  signally  con- 
founded.” 


SECTION  XVI. 

Of  the  Disjunctive  Judgments. 

Disjunctive  Judgments  have  been  defined  to  be 
those  in  which  one  of  two  Categorical  Judg-  Disjunctive 
ments  is  affirmed  to  be  true,  on  the  ground  Judgments, 
that  the  other  is  not  true. 

400.  This  is  called  the  Principle  of  Excluded  Mid- 
dle. It  supposes  two  judgments  so  related  Exduded  Mid. 
as  that  there  is  no  other  judgment  in  the  dle- 
same  matter,  differing  only  in  quantity  and  quality,  or 
both,  and  being  in  a sense  between  them. 

401.  Thus  if  we  take  A and  E,  we  have  the  subal- 
terns between  them ; thus, 

All  A is  B, 

Ho  A is  B ; 

How  “ Some  A is  B,”  is  less  than  “ All  A is  B ” 
(in  affirmative  quantity),  and  more  than  “Ho  A is  B;” 
since  the  latter  has  no  affirmative  quantity.  In  the 
same  way  “ Some  A is  not  B ” stands  between  “ Ho  A 
is  B,”  and  « All  A is  B.” 

402.  Hence  either  of  these  Subalterns  may  be  true 
while  both  the  Universals  in  the  same  quantity  are 
false. 

403.  But  if  we  take  the  Contradictories  there 
such  Middle  Proposition ; — “ Either  All  A is 


None  between 
Contraries. 


is  no 


B, 


or 


Some 


Between  Con- 
tradictories. 


A is  not  B,” — and  “ Either 
Ho  A is  B,”  or  “ Some  A is  B.”  There  is  no  Middle 
Proposition — no  other  Proposition  in  the  same  matter 
which  can  be  true  and  both  of  these  be  false. 

404.  The  same  will  hold  true  of  the  Sub-contraries 
also.  “ Some  A is  B,  and  Some  A is  not  B.” 

How  both  may  be  true — but  there  is  no 

5 


Between  Sub- 
contraries. 


LOGIC. — PAJKT  I. 


98 


[chap. 


Middle  Proposition  between  them ; so  that  if  one  be 
false,  the  other  must  be  true. 

405.  Hence  in  the  first  place  if  we  have  two  Pro- 
in  fere  nee  from  positions  in  the  same  matter,  being  either 
t re  oregomg.  Qontradictories  or  Sub-contraries,  we  may 
affirm  that  one  or  the  other  of  them  is  true,  and 
consequently  we  may  affirm  one  of  them  to  be  true  on 
condition  the  other  is  not. 

406.  But  we  may  have  Disjunctives  in  matter 
either  partly  or  wholly  different ; they  all  come  back, 
however,  as  we  shall  see,  to  the  case  just  stated,  of 
either  Contradictories  or  Sub-contraries.  It  will  be 
necessary  to  investigate  this  relation  a little  further. 

407.  Since  in  nearly  all  cases  of  Disjunctive  Judg- 
ments there  is  one  term  common  to  the  members,  we 

coordinate  may  call  those  terms,  which  are  different  in 
Terms.  each,  for  the  sake  of  convenience,  Coordinate 


the P Proximate  vidual  contained  in  that  genus. 

Genus  give  an  hn-n-p  U A ??  o-nrl  u 
Excluded  Mid-  an(1 

die. 


Terms. 

408.  Any  term  and  its  privative  being  complements 
of  each  other  in  the  proximate  genus,  must  be  contradic- 

positive  and  tories  to  each  other  in  reference  to  any  indi- 

If  then  we 
non-A,” — as  the  two  coor- 
dinate parts  of  a whole, — as  S,  and  Z as  an 
individual  contained  in  that  whole  ; then  “ Z must  be 
either  A or  non-A  ; ” that  is,  it  must  be  included  in 
one  of  the  parts.  But  of  course  the  part  “ non-A  ” may 
be  denoted  by  a positive  term  representing  a coordinate 
species  of  X,  just  as  well  as  by  the  privative  “ non-A.” 
Hence  making  this  substitution,  we  may  have  “ Z is 
either  A or  B.” 

409.  But  again,  if  instead  of  Z denoting  an  indi- 
vidual, we  have  any  term  denoting  a class  compre- 
ifthe  common  h ended  also  under  X,  then  in  one  of  the 
general  term  it  members  of  the  Disjunctive  it  must  be  used 
“huted6 in’one  as  an  undistributed  term.  Thus  let  “ man” 
member.  pe  a wi10le,  and  “ free  ” and  “ slave  ” the 
coordinate  species  ; — let  “Negro”  be  also  a class  com- 
prehended in  “ man,”  and  we  may  say  either  “ all 


n.] 


OF  PROPOSITIONS. SECT.  XVI. 


99 


Negroes  are  free,”  or  “some  Negroes  are  slaves;” 
or  either  “ some  Negroes  are  free  ; ” or  “ all  Negroes 
are  slaves.” 

410.  In  the  second  case  we  may  have  a logical 
whole,  with  a property  common  to  some  of  The  two  Mem- 
the  parts  or  individuals  contained  in  that  ornate  “'sub- 
whole.  This  property  we  may  constitute  ject3- 

the  Differentia  of  a species,  and  then  divide  the  whole 
into  parts  in  such  a way  that  this  property  will  be  pre- 
dicable of  some  one  part  or  of  some  thing  contained 
in  the  whole  which  is  not  that  part.  Thus  let  “ vege- 
tables ” be  such  a whole,  and  “ poisonous  ” such  a 
property,  and  “ cereals  ” a class  of  vegetables,  then 
we  may  say,  “ Either  cereals  are  poisonous,  or  some 
[vegetables]  not  cereals  are  poisonous.”  Or  again, 
let  “ substance  ” be  any  logical  whole,  and  “ matter  ” 
one  kind  of  substance,  and  we  may  say  “ either  mat- 
ter, or  something  which  is  not  matter,  is  eternal.” 
Now  suppose  that  substance  which  is  not  matter  is 
“ spirit,”  and  we  may  say,  “ either  matter  or  spirit  is 
eternal.” 

411.  In  this  case,  as  in  the  preceding,  One  of  the  co- 

/»  , -l  • • j • i i j*  i t - ordinate  terms 

one  oi  the  coordinate  terms  must  be  undis-  must  be  .undis- 
tributed  in  case  they  do  not  stand  for  indi-  irebutedgMen3 

• 1 -i  ° terms. 

viduals. 

412.  If  there  are  more  than  two  coordinate  terms, 
they  must  be  positive  terms,  and  each  denote  More,  than  two* 
its  part  by  differentia  of  its  own.  These  co5rdinates- 
parts,  how  many  of  them  soever  there  may  be,  may 
always  be  reduced  to  two,  by  taking  any  one  as  posi- 
tive, merging  the  Differentia  of  the  others,  and  includ- 
ing them  in  the  privative  of  the  one  assumed  as  positive. 
Thus  the  coordinate  parts,  A,  B and  0,  may  be  reduced 
to  two,  as  “A”  and  “non-A,” — or  “B”  and  “non-B,” 
in  which  case  “ non-A  ” includes  “ B and  C,” — and 
“ non-B,”  “ A ” and  “ C.” 

413.  The  Divided  Whole  may  be  regarded  as  a 
logical,  or  a continuous,  or  a collective  whole,  The  Divided 
and  it  may  be  the  absolute  whole,  or  only  Whole- 


100 


LOGIC. PART  I. 


[CHAP. 


some  assumed  relative  whole.  When,  however,  it  is 
hut  a relative  whole,  some  means  must  he  given  in  the 
Proposition  stating  the  Disjunctive,  to  fix  the  mind 
upon  the  limits  of  the  sphere  of  the  assumed  whole. 
Thus,  “ A wise  lawgiver  must  either  recognize  the  re- 
wards and  punishments  of  a future  state,  or  appeal  to 
a Providence  administering  them  in  this.”  Here  the 
assumed  whole  is  “ wise  lawgivers ,”  and  it  is  divided 
into  two  classes, — (1)  those  who  appeal  to  rewards,  &c., 
in  the  future  life  ; and  (2)  those  who  refer  to  a Provi- 
dence administering  such  rewards  and  punishments  in 
this  state  of  being. 

411.  Instead  of  coordinate  terms  we  may  have  one 
coordinate  and  the  subordinates  of  the  other,  as  in  the 
coordinate  and  following  case : “The  earth  is  either  eternal, 
its  coordinate,  the  work  oi  chance,  or  the  work  ot  an  intel- 
ligent  Author.” 

Here  “ the  origin  of  things  ” is  the  logical  whole. 
The  first  division,  all  things  either  had  an  origin  or 
had  none,  i.  e.,  “ are  eternal.'1'’  But  things  that  had  an 
origin  (the  positive  part,  with  reference  to  the  whole) 
are  divisible  into  two  classes  ; — (1)  those  that  came  by 
chance,  and  (2)  those  that  had  an  intelligent  Author. 
Hence  the  Formula  above  given:  “ The  earth  is  either 
eternal  (had  no  beginning),  or  (its  beginning)  is  from 
chance,  or  from  an  intelligent  Author.” 

415.  But  it  is  not  necessary  that  the  coordinate 
terms  should  denote  coordinate  parts  of  any  division. 
The  coordinate  They  cannot  indeed  be  disparate  parts,  since 
beriDispSmteni>n  there  is  no  necessity  that  any  number  of 
the  same  whole,  disparate  parts  should  include  all  that  was 
comprehended  in  the  Divided  whole.  Privatives,  as 
well  as  Negatives,  are  always  and  only  coordinates 
of  their  Positive.  But  while  disparate  parts  do  not 
Alternate  spe-  necessarily  include  all  the  individuals  of  a 
lire  coordinate  Divided  whole,  Alternate  Species  do  include 
Tunctfve"  judg-  them  all ; and  more  than  that,  they  include 
ment.  some  of  them  twice  at  least.  Every  indi- 

vidual must  be  contained  in  one  of  a set  of  coordinate 


n.]  OF  PROPOSITIONS. SECT.  XVI.  101 

species,  and  can  be  contained  in  no  more  than  one. 
In  Disparate  Species  or  Parts  the  same  individual  may 
be  contained  indeed  in  several,  but  many  may  not  be 
contained  in  any  enumeration  of  Disparate  Parts.  But 
in  Alternate  Species,  while  no  one  may  be  omitted, 
many  may  be  contained  in  several  of  the  species. 

416.  But  although  the  sphere  of  two  Alternate 
Conceptions  is  the  same,  the  matter  is  not.  The  Matter  of 
Hence  the  Differentia  of  several  Alternate  £esernnot  stphee 
Species  is  likely  to  have  many  points  in  same- 
common,  and  must  have  some  that  are  not  so.  How 
suppose  an  individual  to  have  a property  which  we 
know  to  be  a part  of  the  Differentia  of  one  or  two  Al- 
ternate Species,  we  can  predicate  these  species  of  that 
individual  disjunctively.  Suppose  we  have  a collection, 
consisting  of  portraits  of  poets  and  philosophers  alone, 
this  collection  being  one  whole — poets  and  philoso- 
phers would  be  the  Alternate  Species,  including  all 
the  individuals  in  that  whole.  But  they  are  not  Coor- 
dinate Species,  since  the  same  man  may  be  both  a 
poet  and  a philosopher,  conceived  of  from  different 
points  of  view.  Hence  of  any  one  whose  portrait  we 
know  to  be  in  that  collection,  suppose  it  to  be  Cole- 
ridge, we  may  say,  “ Coleridge  was  either  a poet  or  a 
philosopher.” 

417.  But  finally  there  may  be  Disjunctives  with  no 
term  common  to  the  members,  as,  “ Either  A is  B,  or 
C is  D,  or  E is  F,”  &c.  It  is  hardly  possible  pisjUnctjves 
to  enumerate  the  particular  forms  and  rela-  "'ith '“"terms, 
tions  which  the  terms  may  assume  ; since  these  judg- 
ments, as  in  all  preceding  cases,  must  be  parts  of  a 
whole,  and  reducible  to  an  Excluded  Middle.  We  must 
be  able  to  show  that  there  is  no  judgment  except  one 
of  those  enumerated,  that  will  contain  the  truth  which 
the  Disjunctive  is  designed  to  affirm. 

418.  Thus  if  I wish  to  account  for  the  diversities  in 
the  human  race,  I may  say,  “ Either  they  sprang  from 
different  origins,”  or  “ the  diversities  have  been  pro- 
duced by  the  influence  of  climate,  mode  of  life,”  &c., — 


102 


LOGIC. PAKT  I. 


[CHAP. 


or  “ God  must  have  interposed  to  produce  the  variety 
miraculously.”  Here  the  divided  whole  is  “ the  origin 
of  the  diversities  in  the  human  family ; ” and  if  the 
members  of  the  disjunctive  enumerate  all  the  parts  and 
species  to  which  it  can  be  referred,  whether  Coordinate 
or  Alternate,  one  of  them  must  be  true.  If  not,  there 
must  be  some  other  and  Middle  Judgment  which  may 
be  true. 

419.  The  Conditionals  and  the  Disjunctives  are 
compounded  in  two  ways  : 

(1.)  A Conditional  Antecedent  with  a Disjunctive 
compound  of  Consequent,  as,  “ If  A is  B,  A is  either  C or 
D?sjunctires.  & D.” — “ If  the  world  had  a beginning,  it  is 
either  the  work  of  an  intelligent  Author  or  the  product 
of  chance.” 

(2.)  We  may  have  a Disjunctive  Antecedent,  thus, 
“ If  either  A is  B,  or  A is  C,  A is  D.”  This  constitutes 
nnemma.  what  is  called  the  Dilemma — “ If  the  patient 
either  eats  or  abstains  from  food,  he  will  die”  (in  the 
one  case  from  the  effects  of  the  food,  in  the  other  from 
want  of  food). 

420.  In  stating  Dilemmas  it  is  not  uncommon  to 
omit  the  Consequent  to  the  Disjunctive  Antecedent,  as 
being  too  obvious  to  need  explicit  mention. 

421.  Since  Disjunctive  Judgments  always  affirm 
Disjunctive  one  of  the  Members  to  be  true,  on  condition 

verted  into  con-  that  no  one  oi  the  others  is  talse,  we  may 
always  convert  the  Disjunctive  into  a Con- 
ditional by  contra-position  of  one  Member  for  an  Ante- 
cedent, and  using  the  other  or  others,  if  there  be  more 
than  one,  as  Consequent ; thus,  “ Either  A or  B is  C,” 
therefore  “ If  A is  not  C,  B is  C.” 

section  xvn. 

Of  the  Grounds  of  Affirmation. 

422.  The  grounds  upon  which  judgments  are  af- 
firaTuodn.ofAf'  finned  are  reducible  to  three  : — (1)  thePrin- 


XT.] 


OF  PROPOSITIONS. SECT.  XVII. 


103 


ciple  of  Identity  and  Contradiction  ; (2)  Sufficient 

Reason,  and  (3)  Excluded  Middle. 

(1.)  The  first  Principle  is  sometimes  spoken  of  as 
two,  as  in  fact  it  is. 

(a)  Where  the  terms  are  synonymous,  or  the  judg- 
ment affirms  the  identity  of  the  Subject  and  Pril?ciple  0f 
the  Predicate.  Such  is  the  case  in  all  Defini-  Identlty-- 
tions  ; thus,  a triangle  is  “ a figure  with  three  angles,” — 
“ a quadruped  is  an  animal  with  four  feet.” 

( b ) But  there  are  some  terms  the  relation  between 
which  is  so  founded  in  the  nature  of  the  oh-  Princip)e  0f 
jects  for  which  they  stand,  that  the  relation  Contradlction- 
cannot  be  denied  without  destroying  the  conception  of 
one  or  the  other  of  these  objects.  Thus  if  we  say, 
“ every  effect  must  have  a cause  ; ” this  is  not  a judg- 
ment of  identity,  for  “ effect  ” and  “ cause  ” are  not 
the  same.  But  the  affirmation  depends  upon  the  prin- 
ciple of  contradiction  ; that  is,  if  we  say  “ here  is  an 
effect  without  a cause,”  we  at  the  same  time  deny  that 
it  is  an  effect.  If  we  say  that  “ this  triangle  has  but 
two  sides,”  we  deny  that  it  is  “ a triangle.” 

423.  The  force  of  this  ground  of  affirmation  is  well 
exhibited  and  tested  by  resolving  the  judg-  illustration, 
ment  into  a cognition  with  its  modal. 

Thus  in  the  Principle  of  Identity,  we  have  “ Vic- 
toria is  Queen  of  England,”  resolved  into  a cognition 
or  term,  it  is  “ Victoria  Queen  of  England.”  Again, 
a “ triangle  has  three  sides,”  — a “ three-sided  tri- 
angle.” 

424.  Or  to  try  the  principle  of  contradiction,  “ this 
effect  has  no  cause,”  becomes  “ a causeless  effect ; ” — 
“ this  triangle  has  two  sides  only,”  becomes  “ a two- 
sided  triangle.”  In  each  of  these  cases  the  term  and 
its  modal  are  incompatible,  and  taken  together  consti- 
tute an  impossibility. 

425.  (2.)  The  second  ground  of  affirmation  is  called 

sufficient  cause  or  sufficient  reason.  sufficient  reason. 

{a)  This  ground  assumes  that  there  is  no  sufficient 
ground  or  reason  in  the  nature  of  the  matter  itself. 


104 


LOGIC. — PART  I. 


[CHAP 

If  we  say,  “ the  Earth  exists,”  the  will  of  the  Creatoi 
Reason  of  is  considered  as  the  ground  of  the  reality  of 
bemg.  its  being,  if  we  gay^  « all  bodies  gravitate,” 

the  will  of  the  Creator  is  again  considered  the  ground 
of  the  reality  of  the  truth  which  we  affirm.  Or  if  we 
speak  of  the  acts  of  man,  whether  past,  present,  or 
future,  his  will  is  considered  the  sufficient  ground  of 
the  reality  of  these  acts,  the  ratio  essendi. 

(b)  The  means  by  which  we  know  the  reality,  the 
ratio  cognoscendi , may  and  generally  are  in  fact  quite 
Reason  of  different  from  the  ground  of  the  reality  itself, 
knowing.  Take  the  reality  of  gravitation,  for  instance, 
the  ground  of  the  reality  is  the  will  of  God  ; but  our 
means  of  knowing  the  reality  are  experience  and  ob- 
servation. The  reality  of  the  Positive  Institutions  of 
Christianity  depends  upon  the  will  of  God  for  its 
ground,  but  one  means  of  knowing  that  reality  is  Reve- 
lation. 

426.  (3.)  The  third  ground  of  Affirmation  is  called 
Excluded  Middle,  the  Excluded  Middle. 

Between  any  Judgment  and  its  Contradictory  there 
is  no  Middle  or  Third  Judgment. 

TIence  in  any  case  if  we  prove  the  falsity  of  one 
judgment,  this  becomes  the  ground  for  affirming  its 
contradictory. 

427.  But  there  is  especially  one  class  of  Judgments 
which  can  be  affirmed  on  no  other  ground  than  that  of 
Excluded  Middle. 

428.  Such  is  the  case  with  all  affirmative  Proposi- 
Affiimatives  tions  with  negative  Predicates,  and  all  in 
Predicates.11'6  Avhich  the  Predicate  denotes  infinity. 

429.  In  proving  a Proposition  with  an  affirmative 

Copula,  we  include  the  Subject  in  the  sphere  of  the 
proof  of  Nega-  Predicate,  and  this  Ave  do  by  showing  that 
fives.  the  Subject  has  the  Essentia  denoted  by  the 

Predicate.  But  if  the  Predicate  be  negative,  it  is  de- 
noted by  no  matter  of  its  own  ; and  Ave  can  include 
the  Subject  in  the  sphere  of  a negative  Predicate  only, 
by  showing  that  it  does  not  contain  the  Essentia  of  its 


n.]  OF  PROPOSITIONS. SECT.  XVII.  105 

Positive.  That  is,  we  disprove  the  Proposition  with 
the  positive  Predicate  (A  is  B),  and  infer  by  Excluded 
Middle  its  contradictory  that  “ A is  non-B,”  which  is 
at  once  resolved  into  “ A is  not  B.” 

430.  So  also  if  the  Predicate  is  infinite,  as  “ space 
is  infinite  ; ” we  can  affirm  or  prove  our  own  Proof  of  Infi. 
judgment  only  on  the  ground  of  the  falsity  nites- 
of  the  contradictory,  and  by  the  principle  of  Excluded 
Middle.*  God,  Eternity,  and  Space  can  have  no  bounds, 
therefore  they  are  infinite. 


* I do  not  propose  here  to  touch  the  question  between  Sir  William 
Hamilton  and  Scheliing  and  Cousin,  with  regard  to  our  direct  cognition  of 
the  infinite  and  unconditioned.  I am  not  speaking  of  cognition  but  of  proof ; 
the  former  in  their  phrase  is  the  function  of  the  Reason,  the  latter  of  the  Un- 
derstanding. 


5* 


106 


LOGIC. — PART  I. 


[CHAP 


CHAPTER  III. 

OF  SYLLOGISMS. 


SECTION  I. 

Classification  of  Syllogisms. 

431.  A Judgment  is  called  Intuitive  wlien  the  mind 
intuitive  judg-  perceives  and  affirms  the  relation  between 
ments.  two  cognitions  when  they  are  brought  toge- 
ther in  consciousness,  without  the  intervention  or  aid 
of  any  other  cognition. 

432.  But  it  is  not  always  the  case  that  when  two 
cognitions  are  thus  brought  together  in  the  conscious- 
ly^ to  in-  ness,  the  mind  affirms  or  denies  any  kind  of 

tuition.  agreement-  intuitively.  It  may  be  at  a loss 
or  in  doubt.  This  doubt  or  inability  to  see  the  relation 
must  he  the  result  of  the  limited  nature  of  our  faculties. 
Ho  such  doubt  or  hesitation  can  he  felt  by  an  omni- 
scient mind. 

433.  If  now  we  have  two  cognitions,  A and  B,  and 
cannot  see  the  relation  between  them,  so  as  to  consti- 

Deduotive  tute  them  into  a judgment  intuitively,  we 
judgments.  may  see  the  relation  between  each  one  of 
them,  and  a third  term,  as  C for  instance.  We  may 
see  that  “ A ” is  C,  and  that  C is  “ B,”  and  from  these 
two  intuitive  judgments  we  may  have  the  judgment  A 
is  B,  which  in  that  case  is  called  a Deductvoe  Judg- 
ment. 


HI.] 


OF  SYLLOGISMS. SECT.  I. 


107 


434.  Thus  all  deductive  judgments,  which  in  fact 
make  up  the  great  mass  of  human  knowledge  Deductiv# 
and  science,  are  based  upon  intuitive  judg-  eddu“onn1nbtd- 
ments  as  their  premises,  and  may  be  resolved  tlve- 
hack  into  such  intuitive  judgments. 

435.  The  term  which  is  thus  brought  in  as  the 
means  of  forming  the  two  judgments  is  called  the 
Middle  Tekm.  And  when  there  is  but  one  Middle  Terms. 
Middle  term,  the  conclusion  A is  B is  a Deductive  judg- 
ment of  the  first  degree,  or  but  one  step  removed  from 
the  Intuitive.  If,  however,  two  such  Deductive  judg- 
ments become  Premises  to  a Conclusion  still  further 
removed,  there  will  have  been  more  than  one  Middle 
term  and  more  than  two  Intuitive  judgments.  The 
Deductive  judgments,  however,  differ  from  each  other 
only  in  the  degree  of  remoteness  from  the  primary  In- 
tuitive judgments,  which  constituted  the  first  elements 
in  their  deduction. 

436.  The  Deductive  Judgment  or  Conclusion  is 
never  contained  in  or  derived  from  one  of  the  Mediate  infer- 
Premises  alone  by  any  process  of  Imme-  ence- 
diate  Inference.  But  it  is  deduced  from  the  two  Pre- 
mises by  means  of  the  Middle  term,  and  is  therefore  a 
Mediate  Inference. 

437.  By  Syllogism  we  mean  any  combination  of 
two  judgments  as  Premises  in  such  a way  as  syllogism  de- 
that  a third,  different  in  matter  from  either  fined- 

of  them  taken  separately,  results.  The  judgment  so  re- 
sulting is  called  the  Conclusion. 

438.  Syllogisms  are  of  three  kinds ; Categorical, 
Conditional,  and  Disjunctive.  They  are  syllogisms  <u- 
Categorical  when  all  the  Premises  are  Cate-  classes.  in  0 
gorical ; Conditional  when  one  Premise  is  Conditional ; 
and  if  one  Premise  is  Disjunctive , we  call  the  syllo- 
gisms Disjunctive. 

439.  But  Categorical  Syllogisms  are  still  further 

susceptible  of  division,  according  as  the  categorical 
Premises  may  be  either  purely  Categoric,  vfdeTmto  Va- 
Comparative,  or  Probable  Judgments.  rieties- 


108 


LOGIC. PART  I. 


[CHAP. 


440.  In  the  pure  Categorical  Syllogism  there  are 
pure  catego-  three  Propositions,  two  Premises,  and  a Con- 
ncsj  ogism,  cplgjon^  an(j  three  distinct  Terms. 

441.  Of  these  Terms  in  the  simplest  and  most  natu- 
Keiation  of  ral  Formula  (Barbara),  one,  as  individual 
premises  and  or  sub-species,  is  included  m the  second  as 

in  the  Conclu-  .-1-  i ,i  , ■ -..  . it, 

sion.  a species,  and  then  this  second  is  included 

in  the  third  as  the  Genus  — in  the  Premises;  and 
thus  in  the  Conclusion  the  first  is  included  in  the 
third. 

442.  Hence  the  first,  as  its  sjihere  is  the  narrowest, 
is  called  the  Minor  term ; and  the  third,  as  its  sphere 

Names  of  the  is  flic  largest  or  most  comprehensive,  is 
Terms.  called  the  Major  term ; the  other  is  called 
the  Middle  term.  The  Minor  and  the  Major  terms 
together  are  called  the  Extremes. 

443.  But  this  order  is  not  always  observed  ; and  as 
in  some  syllogisms  it  is  impossible  to  determine  which 

Local,  Minor,  term  has  the  widest  sphere,  a more  artificial 
Major  Terms,  denomination  is  given  to  the  terms  tor  ordi- 
nary purposes,  by  which  the  Predicate  of  the  Con- 
clusion is  called  the  Major  term,  and  the  Subject  of  the 
Conclusion  the  Minor  term. 

444.  Hence  the  Nominal  Minor  Term,  whether  the 
real  minor  or  not,  is  the  real  subject  of  the  Syllogism ; 
and  the  Nominal  Major  is  the  real  Predicate  of  the 
Syllogism,  and  the  Syllogism  is  made  for  the  purpose 
of  proving  the  Major  term  as  Predicate  of  the  Minor 
as  its  subject. 

445.  Prom  this  denomination  of  the  Terms  in  a 
Syllogism  the  names  of  the  Premises  are  derived.  As 

Names  of  the  each  term  must  appear  in  two  Propositions, 
premises.  and  as  the  Minor  and  the  Major  appear  in 
the  Conclusion,  the  Middle  term  must  be  found  in 
each  of  the  Premises.  The  other  term  in  each  Pre- 
mise must  therefore  be  either  the  Minor  or  the  Major, 
and  hence  the  Premise  is  called  the  Minor  or  Major 
Premise,  according  as  it  contains  the  one  or  the  other 
of  the  extremes. 


III.] 


OF  SYLLOGISMS. — SECT.  II. 


109 


Thus  S is  M, 

“ M is  P, 

“ S is  P. 

Here  “S  is  M ” is  the  Minor  Premise,  “ M is  P ” is 
the  Major  Premise,  and  “S”  and  “M”  are  the  Ex- 
tremes. 

446.  It  is  usual  in  stating  Formula  to  state  the 
Major  Premise  first.  In  popular  language,  when  we 
are  speaking  of  an  argument,  it  is  usual  to  ..  Princip]e 
call  the  Major  Premise  “ the  Principle  ” & “Instance  " 
upon  which  one  argues  ; and  the  Minor  Term  “ the 
Case”  or  “ the  Instance ” or  “ the  Example”  coming 
under  it. 

447.  The  Conclusion  until  it  is  considered  as  proved,  - 
that  is  until  satisfactory  Premises  have  been  assigned, 
is  called  “ the  Question”  and  is  considered  Question, 
as  yet  sub  questione,  or  under  inquiry. 

448.  As  a Question  it  may  he  stated  in  two  forms, 
What  is  Sf  And  is  S,  P ? 

449.  In  the  former  case  we  are  supposed  not  to 
know  what  is  the  Mai  or  term  ; or  in  other  Question  as 

1 u , to  the  Major 

words,  we  do  not  know  the  proximate  genus  Term, 
to  which  it  belongs,  and  consequently  we  are  said  to 
be  in  doubt  about  the  Predicate,  and  the  Question  is 
concerning  the  Predicate. 

450.  When  the  Question  is  in  the  other  form,  “ Is 

S,  P ? ” we  have  both  terms  given,  and  are  Question  of 

said  to  be  in  doubt  about  the  Copula — or  the  the  Copula- 
question  is  said  to  be  concerning  the  Copula — not  what 
is  the  Predicate,  but  whether  it  may  be  affirmed  of  the 
Subject  or  not. 

451.  If  the  Question  be  concerning  the  Copula  it  is 
answered  by  some  one  of  the  Formula,  which  aue3tiong  of 
we  are  about  analyzing.  But  if  it  be  con-  J,heed b°Fo!muni 
cerning  the  Major  term,  it  can  be  answered  Questions  0f 
only  by  means  of  some  one  or  other  of  the  lnlwlridrS-ei” 
Methods  of  Investigation,  treated  of  below,  vestisation- 
(Part  II.  Chap.  H.) 

452.  In  Categoric  Formula  the  question  concerning 


110 


LOGIC. — PART  I. 


[CHAP. 


the  Copula  is  determined  by  means  of  the  Middle  term, 
office  of  the  which  for  this  purpose  is  used  in  four  differ- 
Middie  Term.  ent  wayS  : — (i)  When  the  Copula  is  expres- 
sive  of  the  identity  of  the  terms  in  either  or  both  the 
Premises  ; (2)  when  it  expresses  a relation  in  Logical 
Four  ways.  Quantity  ; (3)  when  one  or  both  Premises 
are  Comparative  ; (4)  when  one  or  both  are  Probable 
j udgments. 


SECTION  H. 

Of  Pure  Categorical  Syllogisms. 

I.  Of  the  Figure  of  the  Syllogism. 

453.  We  have  already  remarked  that  the  Middle 
term  by  position  is  not  always  the  Middle  in  Logical 
Quantity  between  the  two  extremes,  and  its  office  and 
effect  depends  very  much  upon  its  position.  These 
different  positions  which  it  may  occupy  are  four  in 
Figures.  number,  and  are  called  the  Four  Figures, 
as  follows  : 

1st.  2d.  3d.  4th. 

M is  P.  P is  M.  M is  P.  P is  M. 

S is  M.  S is  M.  M is  S.  M is  S. 

S is  P.  S is  P.  S is  P.  S is  P. 

454.  The  Differentia  of  these  Figures  may  be  thus 
stated  : 

In  the  First  Figure  the  Middle  term  is  Subject  of 
Differentia  of  the  Mai  or  Premise,  and  Predicate  of  the 

tiie  Figures. 

In  the  Second,  it  is  Predicate  in  both  Premises. 

“ Third,  it  is  Subject  in  both. 

“ Fourth,  it  is  Predicate  of  the  Major  and  Sub- 
ject of  the  Minor. 

455.  From  this  it  appears  that  the  Fourth  Figure  is 
only  the  inverse  of  the  First. 

*456.  This  Fourth  Figure  has  been  objected  to  on 
the  ground  that  it  is  unnatural,  and  one 


Fourth  Figure 
objected  to. 


against  which  the  mind  rebels.  On  the 


nx.] 


OF  SYLLOGISMS. SECT.  II. 


Ill 


other  hand  Professor  De  Morgan  thinks  it  the  most 
natural  of  any. 

457.  But  such  considerations  or  arguments  are  of 
no  force.  The  question  is  not  what  is  pleas-  Answers, 
ing,  hut  what  is  possible.  The  Subject  or  Minor  term 
of  an  argument  is  generally  fixed  or  determined  be- 
yond our  control  by  the  circumstances  and  necessities 
of  the  case,  and  we  are  obliged  to  take  the  arguments 
as  we  find  them. 

458.  It  has  been  claimed  also  that  there  is  an 
“ Unfigured  Syllogism  ” by  Mr.  Thompson*  No  unfigured 
Thus  “ Copperas  and  sulphate  of  iron  are  Syllofflsm3- 
identical — sulphate  of  iron  and  sulphate  of  copper  are 
not  identical,  therefore  copperas  and  sulphate  of  copper 
are  not  identical.”  This  he  argues  is  unfigured,  because 
neither  term  in  any  one  of  the  Propositions  can  be  called 
either  Subject  or  Predicate.  But  if  a man  speaks,  he 
must  speak  of  something , and  that  is  “the  Subject;” 
he  must  say  something  of  it,  and  that  is  “the  Predi- 
cate.” Thus  the  Proposition,  “ Copperas  and  sulphate 
of  iron  are  identical,”  is  precisely  tantamount  to  either 
“ copperas  is  sulphate  of  iron,”  or  “ sulphate  of  iron 
is  copperas;”  and  either  term  would  become  Subject 
or  Predicate,  just  according  as  the  one  or  the  other 
object  was  the  subject  of  the  conversation. 

459.  It  will  be  remembered  that  the  Comprehending 
Sphere  is  always  to  be  predicated  of  the  ComPrehend- 
Comprehended  Sphere  in  an  Affirmative  pnrfhendedCom' 
Proposition.  Thus,  If  A is  comprehended  Spheres- 

in  the  sphere  of  B,  we  have  A is  B.  Consequently 
“ A ” and  “ B ” have  spheres  that  are  coincident  to 
the  extent  of  “ A’s  ” comprehensiveness ; and  all  the 
matter  included  in  the  conception  “ B,”  is  ascribed 
to  every  individual  included  in  the  sphere  of  “ A.” 

460.  ISTor  do  we  need  to  make  any  exception  in 
favor  of  those  Propositions  in  which  the  Subject  and 

* “ Outline  of  the  Laws  of  Thought,”  p.  253.  Thompson,  however,  is 
but  following  Sir  William  Hamilton. 


112 


LOGIC. — PAKT  I. 


[CHAP. 


© ® 


the  Predicate  are  Identical,  or  Alternate  Conceptions  of 
identical  the  same  object ; as  “ common  salt  is  chlo- 
spheres.  • ride  of  sodium  ; ” — “ Victoria  is  the  Queen 
of  England.”  In  this  case  the  spheres  of  the  Subject 
and  Predicate  are  identical,  indeed,  but  still  the  Sub- 
ject is  included  in  the  sphere  of  the  Predicate  as  truly 
as  a man  is  included  in  his  own  skin. 

461.  If,  however,  one  sphere  is  excluded  from  an- 
other, as  “ A ” from  “ B,”  then  “ B ” is  the  predicate 

one  Negative  °f  aA”  in  a negative  Proposition,  and  we 
sphere.  have  “ A is  not  B ; ” and  the  spheres  “ A ” 
and  “ B ” have  no  individual  common  to  both. 

462.  And  if  both  Premises  are  Negative  they  will 
Both  spheres  give  us  the  three  spheres,  possibly  exclusive 

collusion.  no  of  each  other,  though  by  no  means  certainly 
so.  Plence  we  shall  have  no  conclusion. 

463.  This  may  be  constructed  thus  : — 

Two  circles,  S and  P,  exclusive  of  each 
other ; this  is  read,  “ S is  not  P.”  Now 
suppose  we  have  another  sphere  M,  and  we  read,  “ M 
is  not  P,”  or  conversely,  “ P is  not  M.”  W e know 
from  this  that  P is  not  in  M,  nor  M in  P,  but  whether 
M is  included  in  S or  not,  we  do  not  know.  It  may 
be  or  it  may  not  for  aught  that  appears. 

464.  The  First  and  Fourth  Figures  being  but  the 
The  principle  converse  of  each  other,  we  may  construct 

of  the  First  and  ,i  • • l i • i A l • 

Fourth  Figures,  the  JL  rmciple  upon  which  their 
validity  depends,  thus  three  circles  as  fol- 
lows : — If  S is  in  M it  must  be  in  P,  and 
some  of  P must  be  in  S. 

(1.)  If  now  the  Middle  term  is  a species  compre- 
hending another,  as  S,  and  wholly  comprehended  in 
Affirmative  another;  as  P,  then  S is  comprehended  in 
conclusions,  p^  an(j  conversely  some  part  of  P must  be 
comprehended  in  S ; that  is,  “ All  S is  P,”  and  “ Some 
P is  S ” 

(2.)  But  if  the  Middle  term  comprehends  one  Ex- 
treme, and  is  not  comprehended  in  the  other,  then  we 


OF  SYLLOGISMS. — SECT.  II. 


113 


m.] 


Principle  of  the 
Second  Figure. 


(D 


“Rn+  No  Affirmative 

_L)UL  LLLL/  Conclusion  in 


can  have  only  a Negative  Conclusion  ; that  Negative  co»- 

. , i -i-i  ^ J l ° . p , • i i elusions  in  First 

is,  the  Extremes  have  no  part  ot  their  spheres  and  Fourth  fi- 
coincident. 

(3.)  Or  suppose  that  the  Middle  term  is  in  the 
larger  circle  and  the  smaller  one  is  not  in  the  Middle, 
then  some  part  of  the  larger  one  must  he  out  of  the 
smaller  one. 

465.  But  in  the  Second  Figure  the  Middle  term  is 
Predicate  in  both  Premises. 

This  we  m qy  construct  as  follows  : — By 
one  large  circle  M,  comprehending  two 
smaller  ones  S and  P ; — S and  P need  not 
cut  each  other,  although  they  may  do  so. 

They  may  also  both  he  in  M without  being 
at  all  coincident  with  each  other  ~ 
fact  of  their  being  both  in  M proves  nothing  Second  Flgure- 
with  regard  to  their  being  coincident.  Hence  we  can 
have  no  Affirmative  Conclusion  by  necessity. 

466.  If,  however,  either  S or  P is  made  coincident 
with  M,  then  of  course  the  other  Extreme  if  the  Middle 
cannot  be  included  in  M without  being  in 

the  other,  and  we  may  have  an  Affirmative  a Concluslon- 
Conclusion. 

467.  But  if  either  S or  P he  in  M,  and  the  other  be 
not  in  it — that  is,  if  one  Premise  be  negative,  S and  P 
cannot  he  coincident,  and  we  shall  have  a Negative 
Conclusion. 

468.  If  the  Middle  term,  whether  species  or  indi- 
vidual, is  contained  in  two  others,  they  must  he  coin- 
cident in  part. 

We  may  construct  this  by  three  circles 
drawn  as  follows  : — If  the  small  circle  M be 
in  both  the  others,  they  must  he  coincident  in 
part,  and  have  enough  in  common  to  include 
M at  least. 

This  explains  the  validity  of  the  Affirmative  Syllo- 
gisms in  the  Third  Figure.  But  if  the  Mid-  „ - . , 
die  term  be  wholly  excluded  from  one  of  the  Third  Fi§ure- 
circles,  that  part  of  the  other  in  which  it  is  contained 


114 


LOGIC. — PAET  I. 


[CHAP. 


must  be  excluded  from  it  also.  But  the  Middle  term 
must  be  excluded  as  a whole  from  one  of  the  circles, 
or  else  they  may  be  entirely  coincident,  and  a part  of 
no  universal  M be  excluded  from  both.  Hence  we  have 
the11  c Third  fT  only  Particular  Conclusions  in  the  Third 
eure-  Figure. 

469.  It  is  also  necessary  that  the  Middle  term  be 
once  distributed  in  the  Premises.  For 

(1.)  In  the  First  and  Third  Figures,  when  it  is  Sub- 
ject in  the  Major  Premise,  if  it  be  not  included  as  a 
whole  in  the  Major  term,  or  excluded*  as  a whole,  the 
Minor  term  may  be  included  in  the  Middle  without 
being  included  in  the  Major  term,  if  the  Premise  is 
affirmative,  or  being  excluded  from  it  if  it  be  negative. 

(2.)  In  the  Second  Figure,  as  we  have  seen,  one 
Premise  must  be  negative,  and  consequently  the  Mid- 
dle term  will  be  distributed  as  Predicate  of  a Negative 
Premise.  Or  if  either  S or  P become  coincident  with 
M,  and  we  have  an  Affirmative  Conclusion,  it  is  be- 
cause in  that  case  M or  the  Middle  term  becomes 
distributed  ; and  in  the  Fourth  Figure  the  same  rea- 
soning applies  as  to  the  First,  only  taken  in  the  inverse 
order. 

470.  It  appears  from  the  foregoing  demonstrations, 
undistributed  that  the  Middle  term  must  be  once  distri- 
buted ; that  is,  taken  as  a whole  in  one  of 

the  Premises.  Otherwise  we  have  the  fallacy  in 
Form  which  is  called  Undistributed  Middle. 

As  an  illustration  of  this  Fallacy  take  the  follow- 
ing : 

“ Moral  virtues  are  habits. 

Skill  in  the  mechanic  arts  is  a habit. 

.-.  Skill  in  the  mechanic  arts  is  a virtue.” 

Both  Premises  in  this  Syllogism  are  true.  But 
there  are  “ habits  ” of  at  least  two  different  kinds — 
moral  virtues  being  habits  of  one  kind,  and  skill  in  the 
mechanic  arts  habits  of  another  kind.  And  since  the 
term  “ habits ,”  being  the  Middle  term,  is  not  distri- 
buted, the  Major  term  is  compared  with  one  part  of 


OF  SYLLOGISMS. SECT.  II. 


115 


m.] 


what  is  included  in  the  Middle  term — that  is,  one  kind 
of  habits — and  found  to  agree  with  it ; and  the  Minor 
term  is  compared  with  the  other  part. 


II.  Of  the  Moods  of  Syllogisms. 

471.  The  Mood  of  a Syllogism  is  that  which  indi- 
cates the  nature  and  order  of  the  Proposi-  The  Mood  of 
tions  which  constitute  it.  As  any  one  of  the  Sylk,s|3ms- 
Four  Judgments  may  be  the  Major  Premise,  Minor 
Premise,  or  Conclusion,  it  is  seen  by  permutation  and 
combination  that  there  may  be  sixty-four  Moods. 

472.  But  by  no  means  all  of  the  sixty-four  Moods 
are  valid  in  any  Figure,  and  of  those  that  are  Nptan  Moods 
valid,  not  all  are  valid  in  all  four  of  the  valid- 
Figures.  Hence  we  must  effect  what  is  called  an 
cibscissio  infiniti — that  is,  a continued  cutting  off  of 
the  several  classes  of  invalid  Moods,  until  we  get  them 
reduced  so  as  to  include  none  that  are  not  valid. 

473.  From  the  Diagrams  and  remarks  upon  them 
just  given,  it  will  appear  with  regard  to  the  Quality 
of  the  Conclusion,  that 

(1.)  If  both  Premises  are  Affirmative,  and  the  Middle 
term  be  once  distributed,  the  spheres  of  the  Quaiityofthe 
Extremes  must  be  in  part  at  least  coinci-  Conclusion- 
dent ; that  is,  the  Conclusion  must  be  Affirmative  also. 

(2.)  If  either  Premise  be  negative,  and  the  other 
affirmative,  and  the  Middle  distributed,  then  the  Ex- 
tremes must  represent  contrary  spheres ; that  is,  the 
Conclusion  will  be  negative. 

474.  In  regard  to  the  Quantity  of  the  Conclusion, 
the  Rule  is  that  “Ho  term  may  be  distri-  Quantityofthe 
buted  in  the  Conclusion,  which  was  not  dis-  Conclusion- 
tributed  in  the  Premises.”  Any  violation  of  this  Rule 
is  a Fallacy  in  Form,  and  is  called  Illicit  Process.  It 
may  be  of  two  kinds,  Illicit  Process  of  the  illicit  process. 
Minor , and  Illicit  Process  of  the  Major. 

We  have  two  cases  in  which  the  Minor  term  may 
be  illicit  in  the  Conclusion. 


116 


LOGIC. — PAJRT  I. 


[CHAP 


(1.)  When  the  Minor  term  is  Subject : Mo  more  of 
ofthe  Minor  the  Minor  term  can  be  either  included  in 
first  case.  or  excluded  from  the  Major  by  means  of  the 
Middle  than  is  included  in  the  Middle  itself. 

(2.)  When  the  Minor  term  is  Predicate  only  that 
second  case,  part  of  it  which  is  coincident  with  the  Mid- 
dle, can  be  included  in  or  excluded  from  the  Major  by 
means  of  the  Middle  ; or  if  the  Minor  term  is  excluded 
from  the  Middle,  then  no  more  of  it  is  excluded  from 
the  Major  by  means  of  the  Middle  than  is  excluded 
from  the  Middle  itself — this  will  be  seen  from  the 
preceding  Diagrams. 

47 5.  As  Affirmatives  do  not  distribute  the  Predi- 
No.uiicitofthe  cate,  there  can  be  no  Illicit  Process  of  the 
conclusions. vc  Major,  except  when  there  is  a Negative 
Conclusion. 

Major!1  of  the  476.  We  may  have  two  cases  : 

(1.)  When  the  Major  term  is  Predicate.  If  the 
Premise  is  Negative  the  Major  term  is  of  course  dis- 
First  case.  ti'ibuted.  But  if  the  Premise  is  Affirmative, 
then  the  Major  term  as  Predicate  must  be  taken  as  a 
whole  ; and  as  such  it  can  comprehend  nothing  which 
is  not  in  the  Middle  term.  But  if  it  be  not  taken  as  a 
whole,  the  Minor  term  may  be  in  that  part  of  the 
Major  which  is  not  occupied  by  the  Middle  term. 

Thus  let  us  have  a large  circle  P,  includ- 
ing M and  something  more.  Thus  S may 
be  in  the  part  of  P,  not  occupied  by  M, 
without  being  in  M,  thus  we  may  have  : 

Mis  P, 

S is  not  M,  and  S may  or  may  not  be  P. 

(2.)  But  in  the  second  case  if  the  Major  term  is 
second  case,  subject  in  the  Premise,  it  must  be  wholly 
included  in  M,  or  S may  be  in  that  part  of  it  which 
is  not  included  in  M. 

Thus  let  us  have  a large  circle  M,  and  PM 
another  P only  part  included  in  it.  Then  /VYA 
S may  be  in  the  part  of  M which  is  not  in-  v>c/ 
eluded  in  P. 


m.] 


OF  SYLLOGISMS. SECT.  II. 


117 


Then  we  have  Some  P is  not  M, 

S is  M, 

and  S may  or  may  not  he  P ; 

Or  suppose  some  in  P only  is  in  M and  the  rest  not, 
and  then  we  may  have — Some  P is  M, 

S is  not  M, 

in  this  case  too,  S may  be  or  may  not  be  P. 

477.  From  what  has  been  said,  it  will  appear, 

1.  That  if  both  Premises  are  negative,  Five  Canon3  of 

we  can  have  no  Conclusion.  validity. 

2.  If  one  Premise  is  negative  the  Conclusion  must 
be  negative. 

3.  If  both  Premises  are  affirmative  the  Conclusion 
must  be  affirmative. 

4.  The  Middle  Term  must  be  distributed  in  one  of 
the  Premises  ; and 

5.  Ho  Term  may  be  distributed  in  the  Conclusion, 
which  was  not  distributed  in  the  Premises.* 

478.  By  the  First  of  these  Rules  the  sixteen  Moods 
with  negative  Premises  are  excluded  from  The  First  ex- 
being valid  in  any  Figure.  By  the  Second,  sixteen 
the  sixteen  with  one  negative  Premise  and  Second,  six. 
affirmative  Conclusions;  and  by  the  Third,  teenmore- 
the  eight  with  affirmative  Premises  and  a m™rd’  eisht 
negative  Conclusion. 

479.  By  the  Fourth  and  Fifth  combined,  all  those 
Moods  in  which  both  Premises  are  particu-  FoUrth  & Fifth, 
lar,  are  excluded ; since  if  both  are  particular  six- 

(and  one  must  be  affirmative),  there  can  be  but  one 
term  distributed  in  the  Premises — and  if  both  Pre- 
mises are  affirmative,  there  will  be  none.  In  this 
case  there  will  be  undistributed  Middle.  But  if  one 
Premise  is  negative  the  Conclusion  must  be  so  too, 

* The  following  hexameters  have  been  found  to  assist  the  memory  in 
retaining  these  fundamental  requirements  of  simple  Categorical  Syllo- 
gisms : 

Distribuas  Medium  : nec  quartus  terminus  adsit 
Utraque  nec  praemissa  negans,  nec  particularis  : 

Sectetur  partem  Conclusio  deteriorem  : 

Et  non  distribuat,  nisi  cum  Praemissa,  negetve. 


118  LOGIC. PART  I.  [CHAP. 

and  then  we  shall  have  either  Illicit  Process  of  the 
Major  or  Undistributed  Middle. 

480.  By  the  operation  of  the  same  rules,  Fourth  and 
six  more.  Fifth,  it  will  be  found  that  if  one  Premise 
be  particular  there  can  be  no  universal  Conclusion. 
(1st)  Suppose  the  conclusion  to  be  A ; in  order  to  that, 
the  Premises  must  be  both  affirmative — and  with  one 
of  them,  Particular  Affirmative — there  will  be  but  one 
term  distributed  in  the  Premises,  if  that  be  the  Minor, 
we  shall  have  undistributed  Middle,  and  if  the  Middle 
we  shall  have  illicit  of  the  Minor.  (3d)  Suppose  the 
conclusion  to  be  E,  one  Premise  must  be  negative,  and 
all  three  terms  distributed  in  the  Premises.  But  there 
are  no  Premises  that  fulfil  this  condition,  except  A 
and  E,  and  O and  E.  But  O and  E are  both  negative, 
and  can  have  no  conclusion  ; A and  E are  universal, 
and  therefore  do  not  come  under  this  rule. 

481.  By  the  same  reasoning  it  will  be  found  that 

ieo.  IEO  will  involve  an  Illicit  Process  of  the 

Major  in  all  the  Figures.*  I 

482.  The  eleven  valid  Moods  are— AAA,  AAI, 
Eleven  valid.  AEE,  AEO,  All,  AOO,  E A^,  EAO,  EIO, 
IAI  and  OAO. 

483.  Hot  all  of  these,  however,  are  valid  in  each 
of  the  Four  Figures  which  we  have  just  described. 

III.  The  Application  of  Moods  to  the  Figures. 

484.  In  the  First  Figures  (1)  if  the  Major  Premise 
Application  of  be  particular  we  can  have  no  Conclusion — 
First  Figure.  for  (a)  if  the  Minor  be  Affirmative  we  should 

* The  Moods  excluded  by  these  Rules  are  : 

By  the  First — EEA,  EEE,  EEI,  EEO,  EOA,  EOE,  EOI,  EOO,  OEA, 
OEE,  OEI,  OEO,  00 A,  OOE,  001,  and  000— (16). 

By  the  Second — EAA,  EAI,  AEA,  AEI,  EIA,  Eli,  IEA,  IEI,  OAA, 
OAI,  AOA,  AOI,  OIA,  Oil,  IOA,  IOI— (16). 

By  the  Third— AAE,  AAO,  AIE,  AIO,  IAE,  IAO,  HE,  100— (8). 

By  the  Fourth  and  Fifth— (1)  OIE,  010,  IOE,  IIA,  III,  IIO— (6). 

“ “ (2)  AOE,  OAE,  IAA,  IEE,  ALA,  EIE— (6). 

“ “ (3)  IEO— (1). 

In  all  16  + 16  + 8 + 6 + 6 + 1 = 63. 


OF  SYLLOGISMS.— SECT.  II. 


119 


m.] 


have  an  undistributed  Middle  ; and  (b)  if  Negative,  the 
Conclusion  must  be  Negative  also,  and  that  would  in- 
volve an  Illicit  Process  of  the  Major. 

(2.)  If  the  Minor  be  Negative  there  can  be  no  Con- 
clusion ; for  the  Major  Premise  would  have  to  be 
Affirmative,  and  that  would  involve  an  Illicit  Process 
of  the  Major. 

Hence  in  the  First  Figure  the  Major  Premise  must 
be  A or  E,  and  the  Minor  A or  I,  and  we  Six  valid-four 
may  have  AAA,  AAI,  EAE,  EAO,  All,  usefuh 
EIO. 

But  as  AAI  and  EAO  have  particular  conclusions, 
when  we  might  have  from  the  same  Premises  an  uni- 
versal one,  they  are  useless  and  so  dismissed  from  fur- 
ther consideration. 

485.  These  Four  Syllogisms  are  called  Barbara , 

Celarent , Darii , and  Ferio*  Names. 

486.  In  the  Second  Figure.  If  both  Premises  are 
Affirmative  we  can  have  no  Conclusion ; second  Figure, 
since  the  Middle  term,  being  Predicate  in  both,  would 
be  undistributed. 


* As  examples  we  may  have  the  following  : 

Barbara.  “ Those  who  derive  benefit  from  every  exertion  of  their  indus- 
try, are  more  likely  to  be  industrious  than  laborers  employed  by  the  day. 
Journeymen  who  work  by  the  piece  derive  benefit  from  every  exertion  of 
their  industry ; therefore  journeymen  who  work  by  the  piece  are  more 
likely  to  he  industrious  than  laborers  employed  by  the  day.” 

Celarent.  “ No  real  hardship  upon  individuals  should  be  authorized  by 
legislative  enactment.  The  impress  of  sailors  is  a real  hardship  upon  indi- 
viduals, therefore  the  impress  of  sailors  should  not  he  authorized  by  legis- 
lative enactment.” 

Darii.  “ Every  thing  which  obstructs  the  free  course  of  justice  deserves 
the  reprobation  of  the  virtuous.  There  are  modes  of  enforcing  the  strict 
letter  of  the  law  which  obstruct  the  free  course  of  justice  ; therefore  there 
are  some  modes  of  enforcing  the  strict  letter  of  the  law  which  deserve  the 
reprobation  of  the  virtuous.” 

Ferio.  “ Those  who  endure  dangers  and  face  death  merely  for  the  sake 
of  acquiring  glory  to  themselves,  without  being  influenced  by  any  desire  to 
benefit  their  country,  are  not  possessed  of  true  fortitude.  But  it  cannot  be 
denied  that  some  of  the  heroes  of  antiquity  endured  dangers  and  faced 
death,  merely  for  the  sake  of  acquiring  glory  to  themselves,  without  being 
influenced  by  any  desire  to  benefit  their  country.  Consequently  several  of 
the  heroes  of  antiquity  were  not  possessed  of  true  fortitude.” 


120 


LOGIC. PAET  I. 


[CHAP. 

And  if  the  Major  Premise  be  Particular  there  can 
be  no  Conclusion,  since  that  would  involve  an  Illicit 
Process  of  the  Major. 

Hence  we  have  in  the  Second  Figure — AEE,  AEO, 
six  valid— four  EAE,  EAO,  EIO,  and  AOO.  But  AEO 
and  EAO  have  particular  Conclusions  when 
we  might  have  universal,  and  hence  they  are  dismissed 
as  useless. 

487.  It  will  be  observed,  that  all  the  Conclusions 
cNo°ncSive  in  this  Figure  are  Negative. 

488.  The  four  valid  and  useful  Syllogisms  in  the 
Examples.  Figure  are  called  Cesar e,  Camestires , Festino , 
and  Baroko .* 

489.  In  the  Third  Figure  there  can  be  no  Universal 
Third  Figure.  Conclusion — for  in  order  to  such  a Conclu- 
sion both  Premises  must  be  Universal ; but  if  both  are 

no  universal  Affirmative,  the  Minor  term  will  be  undis- 
condusions.  tributed,  and  hence  a Universal  Affirmative 
would  be  Illicit  of  the  Minor ; and  if  the  Minor  be 
Negative  the  Major  Premise  must  be  Affirmative,  and 
that  would  give  an  Illicit  Process  of  the  Major  in  a 
Negative  Conclusion.  And  for  the  same  reason  there 
can  be  no  conclusion  if  the  Minor  Premise  be  a Nega- 
tive. 

490.  Hence  in  the  Third  Figure  we  can  have  only 
six  valid  names.  A AI,  All,  EAO,  EIO,  IAI  and  OAO. 


* For  examples  take  the  following  : 

Cesare.  “ No  conscientious  person  wilfully  violates  a solemn  engagement. 
Every  careless  clergyman  wilfully  violates  a solemn  engagement ; therefore 
no  careless  clergyman  is  a conscientious  person.” 

Camestres.  “ All  those  who  are  qualified  for  sea-service  must  possess 
some  knowledge  of  the  arts  of  navigation.  Mere  inland  watermen  do  not 
possess  any  knowledge  of  the  arts  of  navigation ; therefore  mere  inland 
watermen  are  not  qualified  for  sea-service.” 

Festino.  “ No  man  of  sound  sense  can  despise  the  study  of  the  classics. 
Some  modern  pretenders  to  literature  do,  however,  despise  the  study  of  the 
classics  ; therefore  some  of  the  modern  pretenders  to  literature  are  not  men 
of  sound  sense.” 

Barolco.  “ All  the  fixed  stars  emit  light  from  themselves.  Yet  there  are 
some  of  the  heavenly  bodies  which  do  not  emit  light  from  themselves ; 
therefore  some  of  the  heavenly  bodies  are  not  fixed  stars.” 


III.] 


OF  SYLLOGISMS. SECT.  II. 


121 


The  six  Syllogisms  of  the  Third  Figure  are  Darapti , 
Disarms,  Datisi , Felapton , Bokardo , and  Feriso .* 

491.  In  the  Fourth  Figure,  with  A for  Major,  we 
must  provide  for  the  distribution  of  the  Mid-  Fourth  Figure, 
die  term  in  the  Minor  Premise  by  making  that  Premise 
Universal.  If  then  the  Minor  Premise  be  A,  we  may 
have  I for  Conclusion  (A  would  be  illicit  of  the  Major). 
If  the  Minor  Premise  be  E,  we  may  have  E and  O 
for  Conclusions.  But  O is  useless.  Hence  AAI  and 
AEE. 

With  E for  Major  Premise  the  Minor  must  be 
affirmative.  If  A,  we  have  O for  Conclusion  (E  would 
be  illicit  of  the  Minor).  If  it  be  I,  we  have  O also  for 
Conclusion.  Hence  EAO  and  EIO. 

With  I for  Major  we  must  have  A for  Minor  to  dis- 
tribute the  Middle,  and  hence  I is  the  only  Conclusion. 
Hence  IAI. 

With  O for  Major  we  must  have  a negative  Con- 

* Examples  : 

Darapti.  “ To  be  ashamed  of  one’s  birth,  profession,  or  rank  in  life,  has 
been  represented  as  the  fault  of  modesty — whereas  in  reality  it  is  a symp- 
tom of  pride  ; so  that  even  that  which  is  a symptom  of  pride  has  been  repre- 
sented as  the  result  of  modesty.” 

Disamis.  “ Some  practices  which  the  divine  law  allows  are  under  parti- 
cular circumstances  inexpedient.  All  practices  which  the  divine  law  allows 
however  are  in  themselves  consistent  with  holiness  ; therefore  some  things 
which  are  in  themselves  consistent  with  holiness  are  under  particular  cir- 
cumstances inexpedient.” 

Datisi.  “ Every  kind  of  pride  is  wholly  inconsistent  with  the  spirit  of 
religion.  Yet  there  are  several  kinds  of  pride  which  are  highly  commended 
by  the  world,  therefore  there  are  feelings  highly  commended  by  the  world 
which  are  wholly  inconsistent  with  the  spirit  of  true  religion.” 

Felapton.  “ No  conspiracies  against  the  liberty  of  the  country  lay  any 
just  obligation  on  the  conscience.  All  such  conspiracies,  however,  have  the 
nature  of  contracts ; hence  some  contracts  do  not  lay  any  just  obligation 
upon  the  conscience.” 

Bokardo.  “ Some  compositions  of  an  imitative  nature,  calculated  by  sub- 
limity of  idea  and  beauty  of  diction  to  expand  and  delight  the  mind  and  to 
excite  every  noble  passion,  are  not  written  in  verse.  All  such  compositions, 
however,  are  called  poems ; therefore  some  works  justly  called  poems,  are 
not  written  in  verse.” 

Feriso.  “ No  prejudices  are  compatible  with  a state  of  perfection — but 
some  prejudices  are  innocent ; therefore  some  innocent  things  are  not  com- 
patible with  a state  of  perfection.” 


6 


122  LOGIC. PART  I.  [CHAP. 

elusion,  which  would  involve  an  Illicit  Process  of  the 
Major. 

Hence  in  the  Fourth  Figure  we  have  AAI,  AEE, 
Five  valid  Forms.  E AO,  EIO,  and  IAI. 

492.  The  five  valid  and  useful  Syllogisms  in  the 
Fourth  Figure  are,  Bramantvp , Camenes , Bimaris, 
Fesapo , and  Fresison .* 

493.  Of  the  Eleven  valid  Moods,  we  have  AAA 
Recapitulation,  valid  only  in  the  First  Figure  ; AAI  in  the 
First,  Third,  and  Fourth,  but  useless  in  the  First ; 
AEE  valid  in  the  Second  and  Fourth ; AEO  in  the 
Second  and  Fourth,  hut  useless  in  both  ; All  valid  in 
the  First  and  Third  ; AOO  in  the  Second ; EAE  in 
the  First  and  Second  ; EAO  in  all,  but  useless  in  the 
First  and  Second  ; EIO  valid  in  all  Figures ; IAI  in 
the  Third  and  Fourth  ; OAO  in  the  Third. 

494.  In  the  whole,  then,  we  have  Nineteen  valid 
Nineteen  valid  and  useful  elementary  Forms  in  Pure  Cate- 
Syiiogisms.  g0rical  Syllogisms  ; — their  names  have  al- 
ready been  given.  But  for  the  convenience  of  remem- 
bering, especially  for  those  who  understand  Latin 
Prosody,  they  have  been  arranged  into  the  following 
lines  : 

BArbArA,  CElArEnt,  DArll,  FErlOque,  prioris  • 

CEsArE,  CAmEstrEs,  FEstlnO,  BArOkO,  secun- 
dae  ; 

Terlia,  DArAptI,  DIsAmls,  DAtlsI,  FElAptON  ; ' 

BOkArdO,  FErlsOn  habet : Quarta  insuper  addit 

BrAmAntlp,  CAmEnEs,  DlmArls,  FEsApO,  FrE- 
slsOn. 

* Examples : 

Bramanlip.  “All  diamonds  consist  of  carbon — but  all  carbon  is  com- 
bustible ; therefore  some  combustible  substances  are  diamonds.” 

Camenes.  “ All  the  planets  are  opaque  bodies.  No  opaque  bodies  are 
capable  of  transmitting  light  in  any  other  way  than  by  reflection ; therefore 
bodies  capable  of  transmitting  light  in  other  ways  than  by  reflection  are  not 
planets.” 

Dimaris.  “ Some  of  the  inhabitants  of  the  sea  have  antennae  and  horny 
pointed  legs — hut  all  animals  of  this  description  are  insects ; therefore  some 
msects  are  inhabitants  of  the  sea.” 


m.]  OF  SYLLOGISMS. SECT.  III.  123 

The  vowels  printed  in  capitals  will  be  recognized 
as  indicating  the  Mood  of  the  Syllogism,  and  the  con- 
sonants besides  making  out  the  words  serve  another 
purpose,  to  he  explained  by  and  by. 

SECTION  III. 

Of  Indirect  Conclusions. 

495.  There  has  sometimes  been  reckoned  a class  of 
Indirect  Moods,  hut  this  is  unnecessary ; indirect Moods, 
since  all  that  are  reckoned  as  Indirect  Moods  are  merely 
some  one  of  the  Direct  Moods  with  the  Premises  trans- 
posed. 

Thus  for  example,  All  B is  A, 

Ho  C is  B, 

.■.  Some  A is  not  0. 

This  is  simply  Fesapo  with  the  Premises  transposed, 
and  the  Indirect  Conclusion. 

496.  An  Indirect  Conclusion  is  one  in  which  the 
order  of  the  terms  of  the  Direct  Conclusion  Indirect  con- 
is  inverted,  so  as  that  the  Subject  becomes  vereeSfthe'w: 
Predicate,  and  vice  versa ; and  an  Indirect  rect- 
Conclusion  is  valid  when  (1)  it  does  not  change  the 
quality  of  the  Direct  Conclusion ; nor  (2)  distribute 
any  term  in  the  Indirect  Conclusion  which  was  not 
distributed  in  the  Premises. 

497.  It  is  worth  while  to  notice,  however,  that  in 
most  cases  we  may  have  an  Indirect  Conclusion  as  well 
as  the  Direct.*  Thus — Barbara  : 


Fesapo.  “No  vice  is  to  be  admitted  as  a species  of  relaxation  suited  to  a 
Christian.  Every  species  of  relaxation  suited  to  a Christian  consists  of  a 
cessation  from  ordinary  occupations.  Wherefore  there  are  cessations  from 
ordinary  occupations  which  are  not  vice.” 

Fresison.  “ No  fallacious  argument  is  a legitimate  mode  of  persuasion. 
And  some  legitimate  modes  of  persuasion  fail  of  securing  acquiescence ; 
therefore  some  arguments  which  fail  of  securing  acquiescence  are  not  fal- 
lacious.” 

* In  fact  it  will  be  seen  that  all  the  Conclusions  in  the  Fourth  Figure 
are  but  the  Indirect  Conclusion  from  the  same  Premises,  regarded  (by  con- 
sidering'the  Major  term  as  Minor,  and  vice  versa ) as  in  the  First  Figure.” 


124 


LOGIC. — PART  I. 


[CHAP. 


Indirect  Con-  All  T IS  X, 
elusions  in  all  All  7,  i a "V 
Syllogisms.  -tt.il  Li  lb  X , 

.•.  All  Z is  X — or  indirectly,  Some  X is  Z. 

Bramantip  gives  a more  important  Indirect  Con- 
clusion still : 

All  X is  Y, 

All  Y is  Z, 

.*.  Some  Z is  X — or  indirectly,  All  X is  Z. 

In  the  Direct  Conclusion  the  Major  term  appears 
as  undistributed  in  the  Conclusion,  whereas  it  was  dis- 
tributed in  the  Major  Premise. 

498.  Besides  the  above-named  nineteen  Syllogisms, 
any  other  of  the  valid  Moods  may  have  an  incidental 

incidental  va-  validity,  if  its  terms  are  so  distributed  either 
ndity.  by  signs  or  the  nature  of  the  terms,  or  of  the 

matter  of  the  judgment  as  to  secure  us  against  Undis- 
tributed Middle  and  Illicit  Process. 

499.  Again,  if  we  have  two  affirmative  Premises  in 
Analogy  prov-  the  Second  Figure,  both  extremes  are  in  the 
Figure.  bccu"d  same  category — the  Middle  term  ; and  then 
they  must  each  of  them  have  the  Essentia  of  the  concep- 
tion which  the  term  denotes.  They  have  therefore  so 
much  matter  in  common — that  is,  so  many  points  of 
identity,  and  consequently  there  is  an  analogy  between 
the  Extremes. 


SECTION  IV. 

Of  the  Conversion  of  Syllogisms. 

500.  It  has  been  thought  that  all  Mediate  Inference 
could  be  reduced  to  the  celebrated  Dictum  of  Aris- 
Aristotie’s  totle,  called  the  Dictum*  de  Omni  et  Nullo  ; 
D'dum.  that  a Whatever  may  be  predicated  of  a 


* Aristotle  appears  to  have  thought  that  all  Mediate  Inference  could  be 
reduced  to  this  one  Canon.  And  so  by  Conversion  it  can.  But  later  writ- 
ers have  given  us  dicta  for  each  of  the  other  Figures  (Lambert,  Neues 
Organon,  Part  I.  ch.  4,  § 232). 

That  for  the  Second  Figure  is  called  the  Dictum  da  Diverso : “ If  a cer- 
tain attribute  can  be  predicated  (affirmatively  or  negatively)  of  every 


III.] 


OF  SYLLOGISMS. SECT.  IV. 


125 


class  [the  Middle  term],  may  he  predicated  as  Major 
term  of  whatever  is  comprehended  in  that  class,  as  a 
Minor  term  ; and  conversely  whatever  may  he  denied 
of  that  class  may  be  denied  of  whatever  is  compre- 
hended under  it.” 

501.  This  is  substantially  the  same  as  the  first 
Axiom  of  Mediate  Inference  which  we  have  given 
(461) ; and  to  prove  that  all  cases  of  Mediate  Inference 
can  be  reduced  to  it,  various  expedients  have  been  de- 
vised for  reducing  the  Syllogisms  of  the  Second,  Third, 
and  Fourth  Figures  to  Syllogisms  in  the  same  matter 
in  the  First  Figure. 

502.  If  this  were  the  only  object  to  be  gained  in  the 
Reduction  of  Syllogisms,  as  it  is  called,  it  objpct3  of  Re. 
would  hardly  be  worth  the  time  and  pains  duction- 
which  it  costs,  since  the  other  axioms  given  above  are  as 
primary  and  as  satisfactory  as  the  Dictum  of  Aristotle 
itself.  But  there  is  a further  practical  importance  in 
the  Reduction  of  Syllogisms  which  makes  it  worth 
our  while  to  examine  the  laws  and  processes  by 
which  it  can  be  done.  Such  is  the  nature  and  imper- 
fections of  language  that  we  cannot  always  express  our 
judgments  exactly  as  we  would,  and  many  an  expres- 
sion which  suits  all  the  requirements  of  Logic,  fail  to 
meet  the  demands  of  Rhetoric. 

503.  In  order  to  effect  this  Reduction  or  Conver- 
sion, we  need  to  resort  to  Conversion,  Per-  Mean9ofcon- 
mutation,  and  Transposition  of  Premises,  one  version- 

or  the  other  of  them,  and  sometimes  more. 

member  of  a class — any  subject  of  which  it  cannot  be  so  predicated  does  not 
belong  to  that  class.” 

The  Third  Figure  (1)  Dictum,  de  Exemplo : “ If  a certain  attribute  can 
be  affirmed  of  any  portion  of  the  members  of  a class,  it  is  not  incompatible 
with  the  distinctive  attributes  of  that  class ; ” — and  (2)  the  Dictum  de  Excepto  : 
“ If  a certain  attribute  can  be  denied  of  any  portion  of  the  members  of  a 
class,  it  is  not  inseparable  from  the  distinctive  attributes  of  that  class.”  He 
also  gives  what  he  calls  a Dictum  for  the  Fourth  Figure,  which  he  calls 
the  Dictum  de  Reciproco.  But  it  is  hardly  worth  quoting.  The  Fourth  Figure 
is  at  best  but  an  inverse  of  the  First,  and  depends  upon  the  same  Principle 
inverted.  For  the  above  quotations  I am  indebted  to  the  Oxford  edition  of 
Aldrich,  1819,  pp.  72  and  80. 


126 


LOGIC. — PART  I. 


[CHAP. 


Conversion  and  Permutation  of  Propositions  have 
already  been  sufficiently  explained. 

504.  Transposition  consists  merely  in  changing  the 
Transposition  relative  position  of  the  Premises  ; thus,  for 

of  Premises.  7 7 


This  it  will  be  observed  is  not  changing  the  Syllo- 
gism from  one  Figure  into  another.  It  is  merely  writ- 
ing the  Minor  Premise  first  instead  of  the  Major.  Sir 
William  Hamilton  says  that  this  was  generally  done 
for  several  centuries  after  Aristotle.  And  we  shall  see 
by  and  by  that  in  practice,  where  we  are  guided  by 
instinct  and  common  sense,  with  no  regard  to  Logical 
Formulae,  we  usually  state  the  Major  Premise  first 
in  the  Deductive  Methods,  and  the  Minor  first  in  the 
Inductive  Methods. 

505.  But  as  the  transposition  changes  neither  the 
quantity  nor  the  quality  of  the  Premises,  nor  yet  the 
relative  position  of  any  of  the  terms  in  regard  to  the 
laws  of  the  distribution  of  terms  by  Position,  it  can 
have  no  effect  upon  the  concluding  force  of  the  Pre- 
mises. 

506.  In  these  cases  we  obtain  the  result  in  three 
Different  forms  different  forms — we  may  get  (1)  the  same 
oto  um  com  iu-  Qon(qusjon  jn  tpe  Converse  as  in  the  Exposita ; 
or  we  may  get  (2)  one  from  which  that  is  derived  as 
an  Immediate  Inference  ; and  we  may  get  (3)  a Con- 
clusion contradictory  to  that  of  the  Exposita,  but  false  ; 
from  which  of  course  the  truth  of  that  in  the  Exposita 
is  inferred  immediately. 

507.  It  is  with  reference  to  this  process  of  Conver- 
sion of  Syllogisms,  that  the  Consonants  used  in  the 
signification  of  names  that  have  been  given  to  them  are 
§iensName8  !>"  selected;  the  Vowels  are  used  to  indicate 
syllogisms.  the  Mood.  But  the  Consonants  indicate  the 
processes  and  means  of  converting  them  into  Syllo- 
gisms in  the  First  Figure. 


M is  P, 
S is  M, 
'.  S is  P, 


wre  shall  have 


S is  P. 


m.] 


OF  SYLLOGISMS. SECT.  IV. 


127 


All  beginning  with  B,  can  be  proved  in  Barbara. 

“ “ “ C,  “ “ “ u Celarent. 

“ “ “ D,  “ “ “ “ Darii. 

44  44  44  ^ 44  44  44  44 

The  steps  to  be  taken  are  indicated  as  follows  : 

“ m ” denotes  that  the  Premises  are  to  “ m " transposes 

-j  . -•  Premises. 

be  transposed. 

“ s ” denotes  that  in  order  to  reduce  a Syllogism  to 
the  First  Figure,  the  Proposition  signified  converta 
by  the  vowel  before  the  s is  to  be  converted  simpIy- 
simply. 

Thus  the  Minor  Premise  in  Camestres — Flo  Y is  Z, 
is  to  be  converted  into  Flo  Z is  Y. 

“p  ” denotes  that  the  Proposition  indicated  by  the 
vowel  before  it,  is  to  be  converted  by  limita- 
tion, or  per  accidens. 

“ h ” occurs  in  Baroko  and  Bokardo  only.  These 
are  reduced  to  Barbara  by  what  is  called  reductio  ad 
impossibile.  The  reduction  is  effected  by  “ gives  a 
substituting  the  contradictory  of  the  Conclu-  concfus'wnF 
sion  for  the  Premise,  indicated  by  the  vowel  imme- 
diately before  the  “ k,”  and  proceeding  as  before.*  In 
this  way  we  get  a Conclusion  contradictory  to  the  Pre- 
mise for  which  we  have  substituted  the  contradictory  of 
the  old  Conclusion.  If  now  the  new  Conclusion  is  false, 
or  absurd,  or  impossible,  the  old  one  must  have  been 
true.  We  are  in  fact  proving  that  the  Conclusion  is 
O,  by  the  indirect  method  of  proving  that  it  cannot 
be  A. 

508.  In  the  course  of  these  reductions,  it  will  be 
observed  that  the  terms  undergo  several  rela- 
tive changes,  so  that  Major  becomes  Minor, 

&c.,  and  vice  versa.  In  that  case  the  name  of  the  Syl- 
logism ends  in  “s”  or  — -as  “ Camenes,”  “ Bra- 

mantip.”  The  Middle  term  also  in  Baroko  and  Bokardo 
becomes  one  of  the  Extremes. 


“ p converts 
• per  accidens. 


Change  of 
Terms. 


These  rules  have  been  expressed  in  the  following  lines : 
$ vult  simpliciter  verti ; P vero  per  acci- 
M vult  transponi ; K per  impossibile  duci. 


128 


LOGIC. — PAKT  I. 


[CHAP. 


509.  When  in  the  course  of  the  Conversion  or  Re- 
duction of  Syllogisms  we  get  a Conclusion  in  the  same 

quality  as  that  in  the  Exposita  Syllogism, 
the  process  has  been  called  Ostensive  Reduc- 
tion.  But  if  the  Conclusion  be  in  the  opposite  quality, 
Reciuctioad  the  Reduction  is  called  Reductio  ad  hnpos- 
Absurdum.  sibile,  or  Reductio  ad  Absurdum. 

510.  As  examples  in  Ostensive  Reduction,  I will 
Examples.  give  only  a few,  as  follows  : 


Ostensive 

Reduction. 


Cesare 

to 

Celarent. 

No  X is  Y, 

s. 

No  Y is  X, 

cesare.  All  Z is  Y,  the  Minor  stands. 

, All  Z is  Y, 

.-.  No  Z is  X, 

.• 

. No  Z is  X. 

Darapti 

to 

Darii. 

All  Y is  X,  the  Major  stands 

, All  Y is  X, 

Darapti.  All  Y is  Z, 

p- 

Some  Z is  Y, 

.•.  Some  Z is  X, 

'.  Some  Z is  X. 

Bramantip 

to 

Barbara. 

All  X is  Y,  ) 

1 

i All  Y is  Z, 

Brama"-  Y is  Z,  j 

m.  ■ -i 

l Ail  X is  Y, 

Some  Z is  X,  .\ 

Some  X is 

Z,  p Some  Z is 

Felapton 

to 

Ferio. 

No  Y is  X, 

No  Y is  X, 

Felapton.  All  \ is  Z, 

p- 

Some  Z is  Y, 

/.  Some  Z is  not  X, 

. Some  Z is  not 

Fresison  to  Ferio. 

No  X is  Y,  s.  NoYisX, 

Fusison.  Some  Y is  Z,  s.  Some  Z is  Y, 

.•.  Some  Z is  not  X,  .\  Some  Z is  not  X. 

511.  Reductio  ad  Impossibile  is  effected  by  means 
of  Contra-position  and  Excluded  Middle. 

Baroko.  Thus  if  we  have  in  Baroko  : 

Every  star  is  fixed. 

Some  luminous  bodies  are  not  fixed. 

.-.  Some  luminous  bodies  are  not  stars  (such  for  in- 
stance as  planets,  meteors,  &c.) 


in.] 


OF  SYLLOGISMS. SECT.  IV. 


129 


Let  ns  substitute  for  this  Minor  Premise  the  contra- 
dictory of  the  Conclusion  and  we  shall  have  : 

Every  star  is  fixed. 

All  luminous  bodies  are  stars. 

.•.  All  luminous  bodies  are  fixed. 

But  this  Conclusion  is  false,  consequently  the  Mi- 
nor Premise  of  the  first  Syllogism,  Baroko,  its  contra- 
dictory, is  true.  And  if  that  Premise  is  true  (the 
Major  Premise  also),  the  Conclusion  is  irrefragable. 

In  the  same  way  we  may  test  Bokardo. 

512.  Or  again,  we  may  reduce  Bokardo  by  contra- 
position of  the  Major  to  Ferio  ; thus,  Baroko  t0 

All  X is  Y,  Fer‘°- 

Some  Z is  not  Y, 

.*.  Some  Z is  not  X. 

All  X is  Y,  we  may  state  by  contra-position  and 
conversion  in  E. — Xo  non-Y  is  X,  then  we  have  as 
before,  Some  Z is  not  Y or  non-Y, 

.•.  Some  Z is  not  X, 

which  gives  us  the  same  conclusion  in  Eerio  as  we  had 
in  Baroko. 

513.  Again,  we  may  reduce  Bokardo  to  Darii,  by 

permuting,  and  converting,  and  transposi-  Bokardo  to 
tion,  as  follows  : Daril- 

Some  slaves  are  not  discontented.  But 
All  slaves  are  wronged. 

.•.  Some  who  are  wronged  are  not  discontented. 

We  may  have  : 

All  slaves  are  wronged. 

Some  not-discontented  persons  are  slaves. 

.•.  Some  not-discontented  are  wronged. 

514.  This  process  of  Reductio  ad  Impossibile  may 
be  applied  to  all  Syllogisms,  as  well  as  to  Procesg  appli. 
Baroko  and  Bokardo,  on  the  ground  that  if  cable  to  aU- 
we  substitute  for  any  given  Premise  the  contradictory 
of  the  Conclusion,  we  shall  obtain  for  a new  Conclusion 
the  contradictory  of  the  Premise ; or  its  contrary,  in 
which,  of  course,  the  contradictory  is  included. 

6* 


130 


LOGIC. — PART  I. 


[chap. 


Thus  Barbara  to  Bokardo. 

All  Y is  X,  ) by  contra-posi-  ( Some  Z is  not  X, 
Bokardo'0  'All  Z is  Y,  > ti on  of  tlie  Con-  7 All  Z is  Y, 

.•.  All  Z is  X,  ) elusion  becomes  ( .’.  Some  Y is 

not  X. 

Thus  from  Celarent  we  may  have  Disamis  in  the 
Third  Figure,  and  Festino  of  the  Second. 

ceWent  Xo  Y is  X,  Some  Z is  X,  or,  Xo  Y is  X, 
and  Fe”is  All  Z is  Y,  All  Z is  Y,  Some  Z is  X, 

no-  .’.  Xo  Z is  X,  .’.  Some  Y is  X,  .’.  Some  Z is  not  Y. 

515.  It  is  often  very  important  in  general  discus- 
sions to  disembarrass  ourselves  of  the  details  of  Mood 
and  Figure,  and  speak  of  Terms  and  Premises  in  the 
most  general  way ; even  where  the  Differentia  of  the 
Figures  would  require,  if  they  were  recognized  at  all, 
a very  important  modification  of  our  statement. 

516.  For  this  purpose  we  always  consider  an  argu- 
omission  of  ment,  unless  otherwise  expressly  stated,  as 

Figu!'earities  oi  made  in  the  First  Figure,  and  when  we  speak 
of  the  Major  Premise  we  mean  that  which  either  is 
the  Major  in  the  First  Figure,  or  that  which  would 
become  the  Major  if  the  Syllogism  were  converted  into 
that  Figure.  And  for  the  same  purpose  we  consider 
all  Xegative  Propositions  as  Affirmative  with  Xega- 
tive  Predicates,  as  we  have  a right  to  do.  And  hence 
we  may  always  speak  of  that  term  which  either  is  or 
would  become  on  conversion  of  the  Syllogism  into  the 
First  Figure  the  Predicate  of  the  Conclusion,  as  the 
Major  term.  If  the  Conclusion  be  affirmative  that  is  the 
Major  term,  and  if  not  we  substitute  for  the  Predicate 
of  the  Xegative  Conclusion  its  connoted  negative  or 
privative,  which  of  course  becomes  a Major  to  the 
others. 

517.  This  may,  perhaps,  be  thought  to  indicate  a 
indicates  no  looseness  and  uncertainty  with  regard  to  the 

boutYerms. a whole  nomenclature  of  Mood  and  Figure, 
which  does  not  exist.  But  Ave  have  to  take  an  argu- 
ment for  the  most  part  as  Ave  find  it.  And  as  it  thus 
stands,  it  is  no  matter  of  choice  or  uncertainty  which 


HI.]  OF  SYLLOGISMS. SECT.  V.  131 

are  the  Major  and  Minor  terms  by  position.  But  to 
avoid  the  perplexity  and  the  prolixity  of  continued 
repetition  or  detail,  we  may  avail  ourselves  of  the  fact 
that  all  the  Syllogisms  may  he  reduced  to  the  First 
Figure  ; that  is,  the  fact  that  with  the  same  matter  as 
that  given  in  the  Premises,  we  may  prove  the  same 
Conclusion  in  the  First  Figure,  and  thus  adopt  the 
simplicity  and  brevity  of  discussion  which  there  would 
be  if  there  were  only  the  one  Figure. 

SECTION  Y. 

Of  Complex  Syllogisms. 

518.  We  have  thus  far  in  the  investigation  of  the 
laws  and  formula  of  Syllogisms  spoken  only  of  the 
Simple  Categoric  Syllogisms.  Although  this  is  the 
simplest  and  primary  formula,  we  but  sel-  aelJom  meet 
dom  meet  with  them  in  practice.  In  nearly  Pure  and  sim- 

/»  . i , • pie  Formulas. 

every  case  one  or  more  ot  the  terms  is  com- 
plex. Hence  a Syllogism  in  which  one  or  more  terms 
has  a modal,  is  called  a Complex  Syllogism. 

519.  Strictly  speaking  the  simple  term  can  be 
nothing  more  than  a single  word  ; * which  is  simple  Terms, 
either  a noun,  an  adjective,  or  a verb  in  the  Infinitive 
Mood.  In  adjectives  I include  participles  used  ad- 
jectively. 

520.  But  it  often  happens  that  several  words  are 
used  as  the  definition  of  a term  instead  of  Definition  for 
the  term  itself.  Thus  we  have  the  term  a Term- 
Negro — but  instead  of  it  we  may  use  its  definition  in 
any  case — as  “ men  with  dark  skins  and  woolly  hairf 
&c.  Now  suppose  that  we  had  not  the  word  “ Negro  ” 
at  all.  In  that  case  we  should  be  obliged  to  use  its 

* This  must  depend,  however,  somewhat  upon  the  genius  of  a language. 
Perhaps  the  only  exception,  the  only  one  that  I have  noticed  in  the  English, 
is  in  those  words  which  answer  to  the  Aristotelian  category  “ where."  We 
say  a man  is  “in  the  house,” — “on  the  ground,”  &c.,  &c.  We  have  not 
in  this  respect  any  thing  corresponding  to  the  Greek  termination  01  as  in 
aypodi,  oiicoBi,  &C. 


132  LOGIC. PART  I.  [CHAP. 

definition  whenever  we  wish  to  nse  the  conception  as  a 
term  at  all. 

521.  This  is  precisely  the  case  with  regard  to  a 
Necessity  for  a.  large  part,  by  far  the  largest  part  of  the 
conceptions  which  enter  into  our  reasonings.  There  is 
no  precise  term  for  them  ; and  therefore  we  are  obliged 
to  use,  instead  of  the  term,  what  is  really  its  definition. 
The  Definition  gives  first  the  Genus  and  then  the  Dif- 
ferentia one  after  another.  Thus  for  “ Negro  ” we  have 
[genus]  men, — [1st  differentia]  with  dark  skins, — and 
[2d  differentia]  woolly  hair.  Suppose  we  wish  to  speak 
of  those  Christians  who  adhere  strictly  to  their  faith 
and  live  pious  and  devoted  lives,  as  a class  distin- 
tinguished  from  the  rest,  we  have  no  one  word  by 
which  to  denote  the  class.  Consequently  when  we 
want  to  express  the  conception,  we  are  obliged  to  use 
the  definition  for  want  of  a word  to  denote  it. 

522.  In  all  such  cases  Ave  may,  if  Ave  please,  regard 
Definition  a the  Definition  as  the  Term  and  its  Logical 

Mo™hand  IU  Modals,  or  as  a simple  term  for  all  the  ordi- 
nary purposes  of  deduction. 

523.  All  Modals  which  have  any  logical  force  at 
Modais  limit  all,  as  has  been  shoAvn,  either  limit  the  com- 

siveness  of  the  i;>rehensi  veness  oi  the  subject  m reierence  to 
quantity,  or  point  out  some  condition,  or 
time  necessary  to  limit  the  scope  of  the  judgment  in 
order  that  it  may  he  true.  Hence  the  Modal  will  often 
make  the  whole  of  the  difference  between  a Propo- 
sition that  is  true  and  one  that  is  false. 

But  as  Bhetoric  often  requires  some  variety  in  ex- 
pression, the  phraseology  of  Modals  must  often  he 
changed,  and  in  these  changes  Fallacies  often  occur. 

524.  The  Modal  of  a subject  limits  the  scope  of  the 
Modais  of  the  judgment,  by  limiting  the  sphere  of  the 

fhe'tcope of1  the  subject  itself.  Now  from  the  fundamental 
axiom,  that  the  narrower  the  sphere  the 
greater  the  amount  of  the  matter  of  any  conception,  it 
follows  that  more  may  be  predicated  of  a subject  which 
is  limited  by  a modal  than  can  be  predicated  of  the 


nr.]  OF  SYLLOGISMS. SECT.  V.  133 

same  term  without  the  Modal.  Hence  the  dropping  of 
the  Modal  would  in  some  cases  render  the  Proposition 
untrue. 

525.  Suppose  now  that  the  Middle  term  is  first  used 
with  a Modal,  and  is  used  in  the  next  Pre-  Middle  Term 
mise  without  one,  we  have  in  fact  a different  wlth  a Modal- 
term  ; and  it  will  affect  the  formula  differently  accord- 
ing to  its  position. 

Let  us  then  refer  to  the  First  Figure  in  which  the 
Middle  term  is  Subject  of  the  Major  Premise  ln  the  First 
and  Predicate  of  the  Minor.  If  we  drop  the  Figure- 
Modal  in  the  Minor  term  we  enlarge  the  sphere  denoted 
by  it,  and  by  consequence  it  may  become  so  large  that 
the  Major  term  could  not  be  predicated  of  it.  Thus, 

All  true  Christians  enjoy  the  favor  of  God. 

Hypocrites  are  Christians. 

Hypocrites — 

But  here  it  becomes  obvious  that  the  matter  of  the 
Predicate  in  the  Major  Premise  could  not  be  predicated 
of  so  comprehensive  a sphere  as  “ Christians  ; ” that  is, 
“ all  Christians,” — nor  the  Differentia  of  true  Christians 
of  the  subject  of  the'Minor  Premise. 

526.  How  let  us  take  an  example  of  the  opposite 
course : 

All  Christians  believe  in  Christ. 

The  Waldenses  were  true  Christians. 

.•.  The  Waldenses,  &c. 

Here  the  conclusion  is  good.  We  include  the  Minor 
term  by  means  of  the  Modal  in  a narrower  and  com- 
prehended sphere  than  that  which,  as  Middle  term, 
we  had  included  in  the  Major  term  in  the  Major  Pre- 
mise. 

527.  We  have  already  seen  that  the  Middle  term 
must  be  once  distributed  in  the  Premises  of  a Syllo- 
gism, and  in  fact  it  is  distributed  in  both  Premises  in 
two  of  them,  Darapti  and  Felapton.  But  wherever  it 
occurs  as  an  undistributed  term,  it  stands  of  course  for 
a narrower  though  an  undetermined  sphere  than  if  it 


134 


LOGIC. — PART  I. 


[CHAP. 


were  distributed.  We  have  the  following  Rules  for 
Three  Rules,  the  dropping  or  assumption  of  Modals  iii  the 
same  Syllogism. 

(1.)  In  all  cases  where  the  Middle  term  is  undis- 
First  Rule.  ti’ibuted,  as  always  in  the  Minor  Premise  in 
the  First  Figure  for  instance,  we  may  always  make  the 
indeterminate  undistributed  term  a determinate  dis- 
tributed term,  with  a narrower  sphere  than  the  abso- 
lute or  simple  term,  by  joining  to  it  its  appropriate 
Modal.  And  when  the  Middle  is  twice  distributed  as 
in  Darapti,  and  Felapton,  and  Fesapo,  we  may  limit  it 
in  either  Premise  at  discretion,  but  not  in  both  unless 
it  be  with  the  same  Modal. 

(2.)  And  conversely  a Modal  that  was  introduced 
second  Rule,  and  used  with  the  Middle  term  when  used 
distributively,  may  not  be  omitted  where  it  occurs  in 
the  other  Premises  as  an  undistributed  term.  This 
remark,  for  a reason  similar  to  the  one  given  in  case 
of  the  last  rule,  does  not  apply  to  Darapti,  Felapton, 
and  Fesapo,  in  which  the  Middle  term  is  distributed 
in  both  Premises. 

(3.)  And  finally,  if  the  undistributed  Middle  occurs 
Third  Rule.  in  the  Maj or  Premise,  as  in  the  Fourth  Fi- 
gure with  a Modal,  that  Modal  may  be  dropped  when 
the  Middle  term  comes  to  be  used  as  a distributed 
term  in  the  Minor  Premise. 

(4.)  If  in  the  Major  Premise  a Modal  is  used, 
extending  the  comprehensiveness  of  the  judgment  to 
Expansive  all  possible  cases,  then  either  in  the  Minor 

Modais.  Premise  or  in  the  Conclusion  we  may  have 

one  pointing  to  any  special  case  or  class  of  cases, 
included  within  the  comprehensiveness  to  which  the 
Modal  of  the  Major  Premise  extended  it.  Thus  : 

“ Ho  man  is  justified  on  any  pretence  in  taking  the 
life  of  one  with  whom  he  is  living  on  terms  of  con- 
fidence/’ 

“ But  Brutus  was  living  on  terms  of  confidence  with 
Caesar.” 

“ Therefore  Brutus  was  not  justifiable  in  taking 


in.]  OF  SYLLOGISMS.— SECT.  V.  135 

Caesar’s  life  on  the  pretence  which  he  pleaded — of  a 
higher  obligation  to  his  country .” 

(5.)  In  regard  to  the  Minor  term,  if  it  was  used 
without  a Modal  in  the  Minor  Premise  it  Modaisofthe 
was  used  in  its  most  comprehensive  sense  ; MinorTerms- 
hence  if  we  annex  a Modal  in  the  Conclusion  we  sim- 
ply narrow  the  sphere  of  the  subject,  which  as  we  have 
before  seen  does  not  render  the  Proposition  untrue. 
But  if  the  Minor  term  had  a Modal  in  the  Minor  Pre- 
mise, it  may  not  be  omitted  in  the  Conclusion,  since 
that  would  enlarge  its  sphere  and  possibly  include 
thereby  individuals  of  whom  the  predicate  may  not  be 
affirmed. 

(6.)  And  in  regard  to  the  Major  term  the  converse 
holds.  If  there  was  a Modal  in  the  Major  M0daigofthe 
Premise  it  may  be  omitted  in  the  Conclu-  Major  Term- 
sion,  as  by  so  doing  we  enlarge  its  sphere  and  con- 
sequently include  less  matter.  If  therefore  it  was  pre- 
dicable of  the  subject  before  the  enlarge-  Generei  Rule 
ment  of  its  sphere,  then  a fortiori  it  is  after- 
wards.  But  if  the  Major  term  was  in  the  dal- 
Premise  without  the  Middle,  no  Modal  can  be  intro- 
duced into  the  Conclusion,  except  that  which  was 
spoken  of  above  as  changing  the  indeterminate  undis- 
tributed into  a determined  distributed,  denoting  the 
individuals  included  in  the  scope  of  the  subject  as  a 
species. 

528.  We  may  then  lay  down  the  general  proposi- 
tion that  a Modal  may  at  any  time,  and  in  General  Pro. 
any  position  be  attached  to  an  undistributed  aslimpuSn  of  a 
term,  provided  the  Modal  expresses  the  dif-  Modah 
ferentia  or  peculiar  property  of  that  part  of  the  sphere 
of  the  term  which  is  taken  into  the  scope  of  the  judg- 
ment by  its  undistributed  use.  We  thus  convert  the 
indeterminate  undistributed  term  into  a determinate 
distributed  one  with  a narrower  and  comprehended 
sphere. 

529.  It  is  sometimes  a matter  of  doubt  whether  a 
Modal  shall  be  considered  as  belonging  to  the  Subject 
or  the  Predicate  of  a Proposition. 


136 


LOGIC. PAKT  I. 


[CHAP 


Change  of  the 
Modal  from 
Subject  to  Pre- 
dicate, and  vice 
versa. 


Protensive 

Models. 


It  is  not  of  so  much  importance  to  which  it  is  con- 
sidered as  belonging  as  might  at  first  sight  appear,  as 
the  Modal  can  easily  be  transferred  from  one 
term  to  the  other.  Thus,  “ Drowning  men 
catch  at  straws  ; ” — “ Drowning  ” is  here  a 
Modal  of  the  Subject.  But  if  we  say,  “Men 
catch  at  straws  when  they  are  drowning ,”  the  Modal 
is  transferred  to  the  Predicate,  and  the  Proposition 
remains  the  same  for  all  Logical  purposes  ; although 
that  which  was  the  differentia  of  a species  in  the  sub- 
ject becomes  the  conditional  of  the  genus  in  the  Pre- 
dicate, and  vice  versa. 

530.  We  have  yet  another  important  class  of  Mo- 
dals  whose  influence  upon  the  deductive  force  of  the 

Formulae  we  must  consider.  I mean  those 
which  indicate  Protensive  comprehension. 

531.  Such  Modals  seem  rather  to  limit  the  Copula 
than  the  terms  of  a judgment. 

532.  It  is  obvious  that  when  the  Copulas  in  both 
the  Premises  are  taken  with  unlimited  Protension — 

Absolute  pro-  that  is,  with  the  adverb  “ always  ” or  “ uni- 
tension.  versally  ” expressed  or  implied,  we  may 
have  a Copula  in  the  Conclusion  with  the  same  pro- 
tension. 

Let  ns  then  consider  those  adverbial  Modals  which 
limit  the  Protension  without  giving  a definite  limit  to 
it,  such  as  “ sometimes,”  “ generally,”  “ rarely,”  &c. 

533.  It  is  manifest  that  such  Modals  always  limit 
the  Subject,  so  that  a Proposition  in  which  one  of  them 

occurs  cannot  be  regarded  as  universal.  Nor 
is  this  all — they  indicate  that  there  is  no  one 
part  of  the  Subject  of  which  as  a species  the  Predicate 
may  be  affirmed  with  unlimited  Protension.  It  may 
be  affirmed  of  any  or  all  the  individuals  included  in 
the  Subject  at  some  time,  and  at  others  perhaps  it  can 
be  affirmed  of  none  of  them. 

534:.  Now  if  there  is  such  a Modal  in  both  Pre- 
mises, it  is  manifest  that  we  can  have  no 
Conclusion.  For  example : 


Limited 

tension. 


In  both  Pre 
mises. 


m.J 


OF  SYLLOGISMS. SECT.  VI. 


137 


M is  sometimes  P. 
S is  sometimes  M. 


For  it  does  not  appear  but  that  M may  be  included  in 
P precisely  then  when  S is  not  included  in  M,  and 
vice  versa.  The  Minor  term  may  be  included  in  the 
Middle  when,  and  only  when  the  Middle  is  not  in- 
cluded in  the  Major  term. 

535.  But  if  the  Modal  is  in  either  Premise  alone  it 
must  be  in  the  Conclusion  also.  For  if  either  !n  one  Pre. 
Subject  is  in  its  Predicate  only  sometimes,  mise- 
then  the  Conclusion  can  affirm  the  Minor  term  to  be  in 
the  Major  only  “ sometimes .”  And  at  any  particular 
time  it  can  predicate  the  Major  of  the  Minor  only  in  a 
Problematic  or  Probable  Judgment.  The  Conclusion 
with  such  a Modal  in  either  Premise,  therefore,  may 
assume  either  of  the  two  following  forms  : 

S is  sometimes  P ; or 
S may  be  P ; 

that  is,  it  may  be  so  without  contradiction  or  logical 
absurdity. 

536.  We  sometimes  have  a Protensive  Modal,  how- 

ever, when  we  ought  to  have  a differential  Protensive  for 
01'  conditional,  lhus : dai. 

“ Testimony  sometimes  leads  us  into  error. 

The  belief  in  miracles  rests  upon  testimony. 

Hence  the  belief  in  miracles  may  be  only  an  error.” 
Here  for  “ testimony  sometimes  ” we  manifestly  ought 
to  have  “ some  testimony  ; ” that  is,  “ some  kinds  of 
testimony  misleads  us.” 

But  when  we  substitute  “ some  kinds  of  testimony,” 
for  “ testimony  sometimes,”  we  have  not  got  the  full 
force  of  the  Modal  or  the  exact  meaning  of  the  Propo- 
sition. It  does  not  mean  to  affirm  that  there  are  any 
kinds  of  testimony  that  always  mislead.  The  Modal 
of  the  Copula  must  therefore  be  still  retained  in  some 
other  form.  We  may  say,  “ some  kinds  of  testimony 
occasionally  mislead.” 


138 


logic. — part  i. 


[chap. 


SECTION  VI. 

Of  Compound  Syllogisms  or  Sorites. 

537.  The  Syllogism  gives  us  a Conclusion  but  one 
step  further  removed  from  the  intuitive  judgments 
than  the  Premises  themselves,  having  but  one  Middle 
term. 

538.  We  may  however  have  in  the  same  Formula 
sorites.  any  number  of  Middle  terms  with  a deduction 
for  a conclusion,  of  a corresponding  degree  of  remote- 
ness from  the  Premises.  Thus, 

A is  B, 

Bis  C, 

Cis  D, 

.*.  A is  D. 

This  is  called  a Sorites  or  Chain  Syllogism. 

539.  In  the  usual  form  the  Predicate  o.f  each  Prc- 
prderof  Terms  mise  becomes  the  subject  of  the  next  in  a 
Form'.’6  Usual  Universal  Affirmative  Proposition,  until  in 
the  Conclusion  we  have  the  subject  of  the  first  Premise 
for  subject  as  Minor  term,  and  the  Predicate  of  the 
last  for  Predicate  as  Major  term.* 

540.  In  this  Formula  each  successive  term  begin- 
ning with  the  Minor,  has  a wider  and  comprehending 
sphere  until  we  come  to  the  last.  Consequently  what- 
ever may  be  predicated  of  the  last  or  Major  term,  may 
be  predicated  of  the  first  or  Minor  term  just  the  same 
as  if  there  had  been  but  one  Middle  term. 

541.  It  is  manifest  that  as  there  can  be  but  one 
One  Minor  Conclusion,  so  there  can  be  but  one  Major 

Term?6  aiJJor  and  but  one  Minor  Premise.  But  there  may 

* A Sorites,  called  the  Goclenian,  has  been  noticed  also — consisting  of 
Propositions  in  which  the  terms  are  arranged  in  the  inverse  order ; 

Thus  B is  A, 

Cis  B, 

D is  C, 

E is  D, 

A is  E. 

And  this  form  with  the  usual  form  given  above,  are  all  that  have  hitherto 
been  recognized  so  far  as  I know. 


IIX.J 


OF  SYLLOGISMS. — SECT.  VI. 


139 


be  any  number  of  Intermediate  Premises  introduced 
between  the  Minor  and  the  Major  instead  of  intermediate 
one — each  Premise  introducing  a new  Mid-  Premises- 
die  term,  until  the  last  becomes  with  the  Major  term 
either  the  Subject  or  Predicate  in  the  same  Proposi- 
tion. Thus : 

All  Z is  A, 

All  A is  B, 

All  B is  C, 

All  C is  “ 

All  “ is  X, 

All  Is  is  X, 

.-.  All  Z is  X. 


542.  But  there  is  no  necessity  for  confining  the 
Sorites  within  such  narrow  limits  as  have  More  than  one 
usually  been  assigned  to  it.  In  fact  we  can-  formof  Sorite3- 
not  keep  it  within  these  limits.  Other  forms  and  varie- 
ties are  constantly  occurring,  and  the  business  of  Logic 
is  rather  to  account  for  what  is,  than  to  determine 
what  ought  to  be. 

513.  It  is  obvious,  that  if  we  can  introduce  one 
Universal  Affirmative  between  the  Minor  and  Major 
Premise  of  any  Syllogism,  we  can  introduce  any  num- 
ber so  long  as  the  Subject  of  the  one  becomes  the  Pre- 
dicate of  the  next,  or  vice  versa  / in  which  case  each 
new  Middle  term  will  be  once  distributed. 

541.  Hence  in  any  Syllogism,  if  after  transposing 
the  Premises,  we  can  pass  from  the  Minor  Any  syllogism 
Premise  to  an  Universal  Affirmative  and  “anded. e 
from  that  again  to  the  Major  Premise,  we  may  conti- 
nue on  with  any  number  of  Universal  Affirmative  In- 
termediate Premises,  without  changing  the  essential 
character  of  the  Sorites. 

545.  In  this  way  we  find  that  each  of  the  nineteen 
Syllogisms  may  be  expanded  into  Sorites. 

546.  In  the  expansion  of  the  Syllogisms  by  this 
means  we  are  to  regard  only  the  two  Falla-  Cautions  t0  ba 
cies  of  Figure — Undistributed  Middle  and  resarded- 
Illicit  Process.  Each  Middle  term  must  be  distributed 


140 


LOGIC. — PART  I. 


[CHAP. 


once,  and  no  term  distributed  in  the  Conclusion  which 
was  not  distributed  in  the  Major  or  Minor  Premise. 

547.  It  is  sometimes  the  case  that  in  the  expansion 
of  the  Syllogism,  we  are  obliged  to  resort  to  the  inverse 
The  Gocienian  of  the  usual  method,  or  to  what  is  called  the 
pansion.  Gocienian  method.  Thus  in  the  expansion 
of  Camestres : 

JSTo  Z is  A, 

All  B is  A, 

All  C is  B, 

All  X is  C, 

.-.  NoZisX; 

in  which  case  the  Subject  of  each  Intermediate  Pre- 
mise becomes  the  Predicate  of  the  next,  and  the  inverse 
method  would  give  an  illicit  of  the  Major. 

548.  The  introduction  of  a Negative  Intermediate 
Premise  between  two  Affirmatives,  or  of  a Particular 

a Negative  between  two  Universals,  will  have  its  usual 
intermediate,  effects  upon  the  quantity  and  quality  of  the 
Conclusion.  Thus  Darapti  expanded  by  a Negative 
Intermediate  Premise  becomes  : 

All  Y is  Z, 

No  Y is  B, 

All  B is  X, 

Some  Z is  not  X. 

549.  The  Sorites  may  be  resolved  into  as  many 
intSo°sy1iog<ilmsed  Syllogisms  as  it  has  Premises  less  one. 

550.  The  hrst  Premise  containing  the  Minor  term 
of  the  Sorites  is  the  Minor  Premise  of  the  first  Syllo- 
gism, and  the  second  Premise  is  the  Major.  The  Con- 
clusion of  the  first  Syllogism  becomes  the  Minor  Pre- 
mise, and  the  third  Premise  of  the  Sorites  becomes  the 
Major  Premise  of  the  second  Syllogism,  and  so  on, 
each  Conclusion  becoming  Minor  Premise  for  the  next 
Syllogism. 

551.  In  this  way  each  Middle  term  after  the  first 
serves  as  a Major  term  to  establish  the  Minor  Pre- 
mise of  the  Syllogism  in  which  it  is  to  serve  as  a 
Middle. 


OF  SYLLOGISMS. — SECT.  VI. 


141 


m.J 


Thus  the  most  ordinary  form  of  the  Sorites  is  : 

All  A is  B,  First  Example. 

All  B is  C, 

All  C is  D, 

All  D is  E, 

.-.  All  A is  E ; 

which  is  resolved  into  Syllogisms  as  follows  : 


1st.  2d.  3d. 

All  B is  C,  All  C is  D,  All  D is  E, 

All  A is  B,  All  A is  C,  All  A is  D, 

.-.  All  A is  C,  All  A is  D,  .-.  All  A is  E. 

In  this  case  each  of  the  Syllogisms  is  in  Barbara. 

552.  For  another  example  take  the  following : 

All  C is  A, 

C is  not  D, 

All  B is  D, 

.*.  Some  A is  not  B ; which  is  resolved  as 


Second  Exam- 
ple. 


follows : 1st.  2d. 

C is  not  D,  All  B is  D, 

All  C is  A,  Some  A is  not  D, 

.\  Some  A is  not  D.  .*.  Some  A is  not  B. 

The  first  of  these  Syllogisms  will  at  once  be  seen  to 
be  Felapton  (3d  Fig.),  and  the  second  is  Baroko  of  the 
2d  Fig. 

553.  In  most  cases  where  Bramantip  occurs  in  the 
course  of  resolving  the  Sorites  into  Syllo-  The  peculiarity 
gisms,  it  is  necessary  to  use  the  indirect  °fBramant‘p- 
Conclusion  for  the  Minor  Premise  to  the  next  Syllo- 
gism. Thus : All  A is  Z, 

All  B is  A, 

All  FT  is  B, 

All  X is  X, 

.•.  Some  Z is  X. 


(1)  All  B is  A,  (2)  All  X is  B,  (3)  All  X is  X, 
All  A is  Z (ind.  Con.)  All  B is  Z,  Some  Z is  X, 

.•.  Some  Z is  B,  .*.  Some  Z is  X,  .\  Some  Z is  X. 
The  same  thing  occurs  in  Disamis,  Bokardo,  Braman- 
tip, Dimaris,  &c.  &c. 


142 


LOGIC. PART  I. 


[chap. 


554.  In  the  statement  of  the  Sorites,  as  in  fact  in 
the  statement  of  the  Syllogism,  there  is  sometimes  a 

combination  rhetorical  complication  of  terms,  by  means 
BtaLm'ent'" 'of  of  which  the  Subject  is  kept  more  constantly 
sorites.  before  the  mind  than  it  could  otherwise  be. 
This  is  effected  by  converting  each  Proposition  into  a 
single  cognition  as  we  pass  along  according  to  the 
principle  laid  down  [187].  Thus, 

“ All  men  are  mortal. 

All  mortal  men  are  sinners. 

Christ  died  for  all  sinful  men. 

But  the  sinners  for  whom  Christ  died  must  exercise 
faith  and  repentance  towards  God  in  order  to  obtain 
the  benefits  of  Ilis  death  ; therefore  those  who  do  not 
believe  in  Him  and  live  a life  of  faith  and  repentance, 
will  be  left  to  the  full  consequences  of  their  sins.” 

555.  The  only  additional  point  to  be  secured  in 
caution  against  analyzing  such  arguments,  is  that  no  new 
matter.'11011*  term  be  surreptitiously  introduced  by  this 
process  of  accumulation. 

SECTION  VII. 

Of  the  Incomplete  Formula. 

556.  For  the  most  part  in  ordinary  reasoning  one 
Premise  and  sometimes  two  are  suppressed  ; that  is, 
premises  often  they  are  not  stated  in  the  course  of  the  argu- 
suppressed.  ment.  The  reason  is  often  a rhetorical  one. 
It  would  be  tedious  to  be  constantly  repeating  what  is 
so  obvious  as  to  be  known  and  admitted  by  all.  Logic 
however  never  supposes  any  thing  ; it  requires  all  the 
Premises  to  be  stated,  and  hence  we  must  examine 
these  abridged  forms  of  argument. 

557.  They  are  called  Enthymemes , and  may  be  of 

Four  kinds.  foul’  kinds 

(1.)  When  one  Premise  of  a Syllogism  is  omitted. 
First.  In  this  case  we  have  the  Conclusion  and  one 

Premise,  but  the  Conclusion  and  the  Premise  contain 


III.]  OF  SYLLOGISMS. SECT.  VII.  143 

only  three  distinct  terms  ; as,  All  Y is  X,  therefore  All 
Z is  X. 

(2.)  We  may  have  the  Conclusion  and  one  Premise 
with  four  distinct  terms  ; as,  All  A is  B,  second, 
therefore  All  Z is  X.  In  this  case  the  Enthymeme  is 
an  abridgment  of  the  Sorites,  and  the  given  Premise  is 
the  Middle  Premise. 

(3.)  Or  there  may  be  a Conclusion  given  with  more 
than  one  Premise,  and  yet  not  a complete  Third. 
Sorites. 

(4.)  In  the  fourth  case  we  may  have  several  Pre- 
mises in  which  there  is  one  term  common  to  Fourth, 
them  all. 

558.  Enthymemes  with  three  terms  are  easily  com- 
pleted into  Syllogisms.  The  Conclusion  lie-  completion  of 
cessarily  contains  the  Major  and  the  Minor  ofnttt“em&st 
terms.  The  given  Premise  contains  the  Mid-  kind- 

die  term  and  either  the  Minor  or  the  Major  term,  and 
determines  the  position  of  the  Middle  term  as  Subject 
or  Predicate  of  the  given  Premise.  From  this  we  learn 
the  Figure,  the  quality  and  quantity  of  the  Premise 
to  be  supplied. 

Thus,  if  the  Conclusion  he  A,  the  Premises  must 
he  AA. 

If  the  Conclusion  be  E,  the  Premises  must  be  either 
EA  or  AE. 

If  the  Conclusion  be  I,  the  Premises  must  be  either 
AI  or  IA. — (AA  of  course  -would  he  valid  but  not 
necessary.) 

If  the  Conclusion  he  O,  the  Premises  must  be 
either  El,  OA  or  AO. 

559.  Ve  must  always  remember  that  we  have  no 
right  to  supply  a Universal  Premise  in  the  No  Uniyersal 
completion  of  an  Enthymeme  when  a Parti-  dS' ™iissru 
cular  one  would  answer.  This  would  be  13  nectssary' 
attributing  to  him  who  made  the  Enthymeme  what  he 
never  said  and  what  his  argument  does  not  necessarily 
imply.  For  this  reason  no  Enthymeme  can  require  to 
be  completed  in  Darapti,  as  Disamis  and  Datisi  are  in 


144 


LOGIC. — PART  I. 


[chap. 


the  same  Figure,  in  one  or  the  other  of  which  any  En- 
thymeme  with  a Conclusion  in  I in  the  3d  Figure  can 
he  completed. 

560.  If  it  is  found  impossible  to  complete  the  Syl- 
logism— that  is,  to  find  a Premise  that  will  connect  the 
given  Premise  legitimately  with  the  Conclusion,  the 
Enthymeme  includes  or  implies  a fallacy  which  ren- 
ders its  conclusion  worthless  or  worse. 

561.  Of  Entliymemes  with  four  terms  there  can  be 
Enthymemes  only  the  one  variety  given,  except  as  the  dif- 

Terms.  lerence  m quantity  and  quality  may  vary  it : 
All  A is  B, 

.-.  C is  D. 

Any  variation  of  the  relative  position  of  these  terms 
would  produce  no  variety  in  the  Formulae.  It  could 
only  change  the  term  which  a given  letter  represents. 

562.  If  an  Enthymeme  has  four  distinct  terms,  two 
of  them  must  of  course  be  Middle  terms,  and  it  can  be 
completed  into  completed  into  a Sorites  with  three  Pre- 
a sorites.  mises  ; thus,  A is  B,  therefore  C is  D. — “The 
state  punishes  no  man  for  his  religious  opinions,  there- 
fore heresy  is  no  crime.” 

563.  Here  we  have  four  distinct  terms — “ state,” 
“ religious  opinions,”  “ heresy,”  and  “ crime  ; ” and 
the  latter  of  the  two  Propositions  is  given  as  a Conclu- 
sion from  the  former.  Let  us  then  put  A for  state,  B for 
religious  opinions,  C for  heresy,  and  D for  crime,  and 
we  shall  have  : 

All  C is  B, 

No  A is  B, 

All  D is  A, 

No  C is  D,  or  C is  not  D. 

564.  From  which  it  appears  that  the  Enthymeme 
implied  the  two  following  Propositions  : 1st,  the  Minor 
Premise  that  all  “ heresy  ” is  “ religious  opinion ” of 
some  kind  or  another.  — 2d,  for  the  Major  Premise 
whatever  is  a “ crime  ” is  “ punished  by  the  stated  Or 
as  for  rhetorical  purposes  one  would  be  most  likely  to 


m.] 


OF  SYLLOGISMS. SECT.  YU. 


145 


express  the  same  thing  by  contra-position — “ whatever 
is  not  punished  by  the  state  is  no  crime.” 

565.  But  in  the  third  case  we  may  have  the  Con- 
clusion of  a Sorites  with  two  or  more  of  the  Enthymemes 

-r->  lii  j with  more  than 

Premises  given  and  others  suppressed.  four  terms. 

566.  A fundamental  maxim  in  the  completion  of 
these  Enthymematic  Formulae,  is  that  in  No  new  tcrma 
completing  them  no  term  may  be  used  that  introduced- 
was  not  contained  in  the  Elements  of  the  Formulae  that 
were  actually  given. 

If  now  we  have — A is  B, 

B is  C, 

C is  D, 

D is  E, 

E is  F, 

.•.  A is  F ; 

it  is  obvious  that  if  the  1st,  3d,  and  5th  Premises  were 
omitted,  we  should  have  all  the  terms  given,  A,  B,  C, 
D,  E and  F.  Thus,  B is  C, 

D is  E, 

.-.  A is  F, 

and  we  could  easily  restore  the  wanting  Premises  by 
principles  with  which  we  are  already  familiar. 

567.  But  if  one  Premise  were  stricken  out  or  omit- 

ted, the  full  form  could  not  he  completed.  We  should 
have All  B is  C,  j ) All  D is  E, 

A is  F.  \ 01  j All  A is  F ; 


which  would  be  completed  thus  : 

All  A is  B,  or,  All  A is  D, 

All  B is  C,  All  D is  E, 

AH  C is  F,  All  E is  F, 

All  A is  F,  All  A is  F. 

568.  As  the  Middle  term  is  usually  a general  term, 
that  is  a term  denoting  a class,  it  is  obvious  Enthymemes 
that  the  result  will  be  the  same  if  in  a sue-  stated 
cession  of  Propositions  we  compare  either  of  dlvldually- 
the  Extremes  with  the  individuals  of  which  the  Middle 
term  is  composed,  as  if  we  should  compare  that  Ex- 


7 


146 


LOGIC. — PAET  I. 


[chap. 


treme  with  the  Middle  term,  as  a Whole  in  a single 
ciussificatory  Proposition,  this  gives  a Classificatory  For- 

Formula.  muld. 

569.  Thus  let  M he  a genus  consisting  of  the  indivi- 

duals a , b,  c,  d and  e,  we  may  thus  predicate  P of  each 
of  these  ; as,  a is  P, 

b is  P, 
g is  P, 
d is  P, 
e is  P ; 

and  then  as  whatever  may  be  predicated  of  all  the 
individuals  of  a class,  whether  genus  or  species,  may 
be  predicated  of  the  class,  we  may  have  for  these  seve- 
ral Propositions,  M is  P ; since  by  the  supposition  M 
is  the  general  term  whose  comprehended  individuals 
are  a , b,  c,  d and  e.  With  “ M is  P ” we  may  have 
the  Conclusion  S is  P — the  two  constituting  an  Enthy- 
meme. 

570.  This  it  will  be  seen  by  and  by  is  the  Form  in 
The  Formulas  which  Induction  is  usually  stated  ; thus, 

of  induction,  the  wolf,  the  fox,  the  cat  are  individuals 

which  make  up,  or  at  least  represent  the  class  of  ani- 
mals called  Oanidce , or  animals  with  canine  teeth, 
blow  we  may  say  : 

The  wolf  is  carniverous, 

The  fox  is  carniverous, 

The  cat  is  carniverous, 

.•.  the  Canidae,  or  animals  with  canine  teeth,  are  car- 
niverous. 

571.  It  will  follow  of  course  on  the  same  principle, 
cumulative  that  if we  predicate  the  several  individuals 

Formula.  0f  which  the  Middle  is  composed  of  the  Mi- 
nor term  individually,  we  may  predicate  the  Middle 
itself  of  that  Minor,  thus  : 

S is  a , 

S is  b, 

S is  c, 

S is  d, 

Therefore  S is  M. 


m.]  OF  SYLLOGISMS. — sect.  vn.  147 

572.  This  is  the  Formula  of  what  is  called  the 
Cumulative  Argument. 

573.  The  Cumulative  Formula  differs  from  the  In- 
ductive in  that  the  Cumulative  Formula  is  an  Enthy- 
meme  with  the  Major  Premise  suppressed. 

Thus  in  Mr.  Webster’s  argument  in  the  case  of  the 
White  murderers,  we  have  : 

“ The  prisoner  was  at  the  place  at  the  time  of  the 
murder. 

“ He  participated  in  the  motives  which  led  to  the 
commission  of  the  murder. 

“ He  owned  and  usually  carried  with  him  the 
weapon  with  which  the  murder  was  committed. 

“ He  shared  in  the  means  which  were  afterwards 
taken  to  divert  attention  from  those  who  were  actually 
engaged  in  committing  the  murder. 

.*.  the  prisoner  is  guilty.” 

574.  It  will  often  happen,  as  in  this  case,  that  there 
is  no  one  term  in  the  language  that  will  de-  sometimes 
note  the  genus,  which  these  several  terms  ^'fterm "brlhe 
predicated  of  the  Subject  taken  as  a Logical  Middle- 
Whole,  would  constitute.  But  whether  there  is  such 
a term  or  not  they  must  be  considered  as  making  such 
a Whole,  and  one  too  which  may  be  predicated  of  the 
Minor  in  the  Inductive  Formula,  and  of  which  the 
Major  term  may  be  predicated  in  the  Cumulative  For- 
mula. In  the  case  alluded  to,  Mr.  Webster  argued  his 
Major  Premise  at  some  length  ; thus,  “ Whoever  was 
present  when  the  murder  was  committed  had  a motive 
and  the  means  for  committing  it,  and  subsequent  to 
its  commission,  endeavored  to  foil  all  attempts  at  dis- 
covering the  murderer,  must  be  held  guilty.”  Here 
plainly  for  want  of  a single  term  of  which  to  predicate 
“ guilty,”  he  enumerates  the  individuals  of  which  it  is 
composed — in  short  describes  its  sphere. 

575.  In  both  of  the  above-named  Formulae  it  is 
necessary  that  the  Premise  which  is  thus  Must  mum- 
individually  stated,  should  enumerate  all  ordinate  pans0' 
the  coordinate  parts  of  the  Middle  term  as  a Logical 


14:8  LOGIC. — PART  I.  [chap. 

Whole,  otherwise  it  is  manifest  that  we  may  have  an 
Undistributed  Middle. 

SECTION  VIII. 

Of  Epichirema. 

576.  Besides  the  Sorites  we  have  sometimes  For- 
mulae in  which  there  is  a Proposition,  which  is  redun- 
dant so  far  as  the  purposes  of  that  Formula  are  con- 
cerned. These  Formulae  have  been  called  Epichirema. 
The  Propositions  serve  an  important  purpose,  and  are 
called  either  Pro-Syllogisms  or  Epi-Syllogisms. 

577.  The  Pro-Syllogism  is  a Proposition  thrown  in 
pro  syiiogism.  either  before  or  after  one  of  the  Premises  as 
a Premise  to  that  Premise  ; and  of  course,  therefore,  is 
a Premise  which  with  the  given  Premise  for  a Conclu- 
sion constitutes  an  Enthymeme.  For  example  : “ Con- 
fidence in  promises  is  essential  to  the  intercourse  of 
human  life  (because  without  it  the  greatest  part  of  our 
conduct  would  proceed  upon  chance).  But  there  could 
be  no  confidence  in  promises  if  men  were  not  obliged 
to  perform  them  ; therefore  the  obligation  to  perform 
promises  is  as  essential  as  the  intercourse  of  human 
life.” — ( Paley .) 

578.  Flere  the  Pro-Syllogism,  which  is  thrown  in  to 
confirm  the  Major  Proposition,  is  enclosed  in  the  paren- 
thesis. 

Again,  we  sometimes  have  a Conclusion  stated  im- 
Epi-syiiogism.  mediately  after  the  Conclusion  of  a Formula, 
and  to  which  the  Conclusion  of  the  Formula  is  designed 
to  serve  as  a Premise.  This  is  called  an  Epi- Syllogism. 

As,  Y is  X, 

Z is  Y, 

.-.  Z is  X, 

.-.  Z is  W, 
or  .-.  M is  X. 

579.  Here  the  Conclusion  serves  as  a Premise  to 
the  Epi-Syllogism,  and  the  two  together  are  an  Enthy- 
meme. 


m.] 


OF  SYLLOGISMS. — SECT.  IX. 


14:9 


SECTION  IX. 

Of  Compound  Judgments  in  Syllogisms. 

580.  We  have  seen  in  a previous  Section  how  any 
compound  Proposition  may,  for  all  the  purposes  of  the 
Syllogistic  Conclusion,  be  regarded  as  a simple  Propo- 
sition with  a Modal. 

581.  Such  a process  of  course  implies  that  the  Judg- 
ments into  which  the  Compound  Proposition  may  be 
resolved,  are  either  all  false  or  all  true  toge-  AI1  the  sim. 
ther.  When  they  are  thus  regarded  how-  SlustJbe!^lnor 
ever  as  simple  Propositions  with  Modals,  false  together' 
we  proceed  with  them  as  though  they  neither  contained 
or  implied  more  than  the  one  Judgment,  and  the  law 
concerning  Modals  already  stated  must  be  observed. 

5S2.  When  either  of  the  Premises  is  a Compound 
Proposition  thus  regarded  as  a simple  one, 

,i  i n n May  have  a 

the  Conclusion  may  ot  course  be  a Com-  compound con- 
pound  of  the  same  kind;  only  that  it  will 
appear  as  a Modal  Proposition  containing  one  modified 
judgment.  This  Proposition  may  be  again  resolved 
back  into  its  component  simple  judgments  by  the  same 
process,  though  in  the  inverse  order — as  it  has  been 
resolved  from  a Compound  into  a simple  Modal  Propo- 
position.  Thus,  M is  (X  and  P), 

S is  M, 

.-.  S is  (X  and  P). 

But  the  Major  Premises  may  be  resolved  into  “ M is 
X,”  and  “ M is  P.”  So  also  the  Conclusion  into  “ S 
is  X,”  and  “ S is  P.” 

583.  But  it  is  sometimes  the  case  that  the  Conclu- 
sion depends  upon  only  one  of  the  simple  0uIy  OIie  of 
judgments  contained  or  implied  in  the  Com-  us|dJuiu”“ome 
pound  Proposition.  In  that  case  whether  the  cases- 
Compound  be  either  copulative  or  discretive,  we  must 
treat  the  judgment  which  is  not  taken  into  the  scope  of 
the  Syllogism  in  the  Premises,  as  in  no  other  way  be- 
longing to  it  or  affecting  it.  It  is  a mere  rhetorical 
sumlusage. 


150 


LOGIC. — PART  I. 


[chap. 


584-.  Causal  Propositions  are  properly  Entliymemes, 
causal  propo-  containing  a Conclusion  and  one  Premise. 

The  Causal  Judgment  may  be  regarded  as 
merely  a Pro-Syllogism.  We  may  also  regard  it  as  a 
mere  Modal ; thus, 

“Christians  are  happy  because  they  have  faith ; 

The  early  martyrs  were  Christians  : 

the  early  martyrs  were  happy  because  they  had 
faithS 

585.  When  the  Major  Premise  is  a Causal,  if  the 
Minor  affirms  the  cause  of  any  new  Minor  term,  the 
Conclusion  may  affirm  the  Predicate  of  the  Major  Pre- 
mise of  the  new  Minor  term.  Thus  we  may  say  : 

“ Christians  are  content  with  their  lot,  because  they 
have  faith  j 

The  Early  Martyrs  had  faith  : 

.*.  the  Early  Martyrs  were  content  with  their  lot.” 

586.  Now  if  this  Conclusion  he  not  true,  it  must  be 
either  because  the  Minor  Premise  is  a non  vera  (un- 
true), or  because  the  main  Proposition  in  the  Major 
Premise,  “ Christians  are  content  with  their  lot,”  is 
untrue  ; or  finally,  because  the  cause  assigned— “ be- 
cause they  have  faith,”  is  not  the  cause,  is  a non  causa 

PRO  CAUSA. 

587.  The  Discretive , Exceptional , and  the  Exclusive 
Discretives,  Ex-  Propositions,  as  has  been  seen,  agree  in  con- 
Exclusives.  taming  or  implying  judgment  ot  one  qua- 
lity while  they  express  a judgment  of  another.  These 
judgments  have  one  term  common  to  them  both.  The 
Exceptional  affirm  the  Predicate  of  the  subject  and 
deny  it  of  all  other  subjects.  The  Exclusives  include 
the  subject  in  the  Predicate  and  exclude  all  other  sub- 
jects from  it.  The  Discretives  affirm  one  Predicate 
and  deny  another  of  the  same  subject. 

588.  Hence  these  classes  of  Propositions  may  be 
regarded  as  negatives  or  affirmatives,  according  as  we 
involve  in  our  Syllogism  the  one  or  the  other  of  the 
judgments  contained  in  them.  Thus  for  a Discretive  : 


TTT-]  OF  SYLLOGISMS. — SECT.  X.  151 

A is  B,  but  A is  not  C, 

S is  A,  S is  A, 

.-.  S is  B,  .•.  S is  not  C. 

For  an  Exceptive  take  the  following  : 

“ All  races  of  men  except  the  Anglo-Saxons  have 
failed  to  sustain  free  Institutions  ; Examples. 

The  Canadians  are  Anglo-Saxons  : 

.*.  the  Canadians  have  not  failed,  &c.” — 
or  with  a Negative  Minor  Premise  : 

“ The  Mexicans  are  not  Anglo-Saxons  ; 

.*.  the  Mexicans  have  failed,  &c.” 

In  the  first  case  the  Affirmative  Judgment  is  used 
as  Major  Premise,  and  in  the  second  the  Negative. 

589.  Again,  in  the  case  of  an  Exclusive,  we  have 
the  same  phenomenon  : 

“ Water  is  the  only  thing  in  the  sea  ; 

Fish  live  in  the  sea  : 

.•.  Fish  live  in  the  water.” 

“ Water  is  the  only  thing  in  the  sea  ; 

Hot-blooded  animals  do  not  live  in  water  : 
Hot-blooded  animals  do  not  live  in  the  sea.” 

In  the  above  examples  we  have  an  Affirmative 
Conclusion  in  the  2d  Figure,  and  a Negative  Conclusion 
with  an  Affirmative  Major  Premise  in  the  1st  Figure. 

SECTION  X. 

Of  Comparative  Syllogisms. 

590.  It  has  been  usual  to  regard  Comparative  Judg- 
ments as  but  Pure  Categoricals  with  Modals.  Force  of  Mo_ 
But  the  Modals  of  Comparative  Judgments  *1^“  |yX: 
exert  an  influence  upon  the  Formulae  essen-  gisms- 
tially  different  from  that  of  any  class  of  Modals  yet 
considered.  Comparative  Judgments,  as  already  shown, 
are  Formally  different  from  any  other;  and  constitute 
a class  by  themselves  with  differentia  peculiarly  their 
own. 


152 


LOGIC. — PART  I. 


[CHAP. 


Thus  we  may  have — M is  P, 

S is  greater  than  M, 

.•.  S is  greater  than  P. 

Here  we  have  a Modal  to  the  Middle  term  in  the 
Minor  Premise,  and  none  to  it  in  the  Major.  We 
have  also  a Modal  to  the  Major  term  in  the  Conclu- 
sion and  none  in  the  Major  Premise  ; and  yet  we  see 
at  once  that  the  Formula  is  valid. 

Again  we  may  have  different  Modals  in  each  Pre- 
mise, as  : Y is  greater  than  X, 

Z is  equal  to  Y, 

.*.  Z is  greater  than  X. 

591.  Comparative  Syllogisms  are  of  three  kinds  : — 
Three  kinds.  (1)  Simple  Comparatives  in  Continuous 
Quantity  ; (2)  Comparatives  in  which  the  difference 
of  intensity  is  regarded  as  cause ; (3)  Comparatives 
of  time,  place,  manner,  &c. 

I.  Simple  Comparatives. 

592.  In  Continuous  Quantity  the  reasoning  depends 
upon  the  following  Axioms  : 

(1.)  Axiom  of  Equality.  If  any  two  things  are 
First  Axiom,  each  equal  to  one  and  the  same  third  thing, 
they  are  equal  to  each  other.  Thus,  If  A and  B are 
each  equal  to  C,  A and  B are  equal  to  each  other. 

(2.)  Axiom  of  Difference.  If  of  any  two  things  one 
second  Axiom,  is  greater  and  the  other  less  than  or  equal 
to  a common  third,  then  the  one  is  greater  than  the 
other.  Thus,  If  A is  greater  than  C,  and  B is  equal 
with  C,  A is  greater  than  B ; or  if  A is  less  than  C,  and 
B is  equal  with  it,  A is  less  than  B. 

(3d.)  If  two  terms  are  both  either  greater  or  less 
Third  Axiom,  than  a common  third  term,  no  conclusion 
can  be  drawn  concerning  them  by  means  of  a compari- 
son with  that  third  term. 

593.  If,  however,  in  cases  coming  under  the  last 

Application  of  Axiom  we  introduce  Discrete  Quantity  also, 
uty.  so  as  to  express  how  much  greater  or  less 


in.] 


OF  SYLLOGISMS. — SECT.  X. 


153 


each  of  the  terms  compared  are,  than  that  with  which 
they  are  compared,  a conclusion  can  he  drawn — thus, 
three  is  two  less  than  five,  and  six  is  one  more.  Hence 
six  is  three  more  than  three. 

The  two  terms  of  which  we  speak  in  these  Axioms 
are  the  Extremes,  Minor  and  Major,  and  the  common 
third  term  is  the  Middle  term. 

591.  We  shall  greatly  facilitate  our  examination 
of  the  Formulae  of  Continuous  Quantity  by  introducing 
a method  of  notation  somewhat  similar  to  Explanation  of 
Sir  William  Hamilton’s, — in  which  we  will  sign3- 
denote  comparisons  which  imply  the  equality  of  the 
two  Extremes  of  a Comparative  Judgment,  by  parallel 
lines  drawn  between  the  Subject  and  the  Predicate,  as 
S = P,  “ S is  equal  to  P.”  Comparisons  of  Inequality 
will  be  denoted  by  the  Convergent  when  the  Subject 
is  larger  than  the  Predicate,  and  by  the  Divergent 
when  it  is  the  reverse.  Thus,  S fc=-  P,  “ S is  larger 
than  P ; ” and  S < P,  “ S is  smaller  than  P.” 

595.  The  fact  that  Comparatives  of  Inequality  are 
converted  by  transposition  of  terms  and  convergent* 
changing  of  the  Comparative  Modal  for  that  convirfe  ‘of 
which  is  in  the  same  degree  of  comparison  eachottier- 
as  the  other  side  of  the  Positive,  is  indicated  by  the 
fact  that  the  Convergent  and  the  Divergent  are  but  the 
converse  the  one  of  the  other. 

596.  But  the  Indefinite  Comparisons,  as  we  have 
seen,  affirm  only  that  the  Subject  is  as  great  Notationofthe 
as  the  Predicate.  We  might  therefore  al-  Indefillite- 
ways  represent  these  Comparisons  by  the  sign  of 
equality — only  remembering,  however,  that  such  Pro- 
positions cannot  be  converted. 

597.  But  as  such  a mode  of  notation  may  lead  to 
confusion  in  some  cases,  it  will  be  well  to  denote  the 
Indefinite  Comparisons  by  two  straight  lines  crossing 
each  other,  thus  -I — . 

598.  How  since  in  Comparisons  of  Equality  the 
compared  and  the  standard  of  the  compari-  comparisons 
son  are  equal  to  each  other,  it  will  follow  of  Equality. 

7* 


154 


LOGIC. PART  I. 


[chap. 


that  if  both,  or  all  the  Premises  are  Comparisons  of 
this  kind,  all  Moods  and  all  Figures  must  be  valid. 

1st,  A = B,  2d,  A = B,  3d,  B = A,  4th,  B = A, 
B = C,  C = B,  B = C,  C = B, 
.-.  A = C,  .-.  A = C,  .*.  A = C,  .-.  A = C. 

599.  But  if  both  are  Comparisons  of  Inequality, 
of  inequality  unless  they  can  be  so  converted  or  read  as  to 
e”  of* theresame  come  into  the  1st  or  4th  Figure,  and  of  the 

same  intensity,  there  can  be  no  Conclusion 
except  by  means  of  Discrete  Quantity.  Thus : 

2d,  A > B,  3d,  B < A, 

C > B,  B < C. 

In  both  these  cases  the  Premises  offend  against  the 
Third  Axiom. 

600.  But  if  the  intensity  be  unlike  in  the  2d  or  3d 
of  opposite  Figures  we  may  have  a Conclusion.  In  that 

case  the  Premise  may  be  read  either  in  1st 
or  4th  Figures,  and  so  brought  under  the  2d  Axiom — 
the  Axiom  of  Inequality  ; thus, 

A=~B, 

C<B, 

becomes  “A  is  greater  than  B,”  and  “ B is  greater 
than  C.”  Hence  we  may  have  the  Conclusion  “ A is 
greater  than  C,”  or  A ==-  C. 

601.  If  the  Premises  are  read  in  the  4th  Figure, 
premises  read  the  Conclusion  will  be  of  the  opposite  inten- 

Figure.  Iourth  sity  from  that  in  the  Premises,  or,  which  is 
the  same  thing,  the  Conclusion  here,  as  in  Logical 
Quantity,  will  be  the  converse  of  that  in  the  1st  Fi- 
gure ; thus, — 1st,  M=>P,  4th,  P <1, 

S >M,  M<  S, 

.-.  S >P,  S=>P. 

602.  If  the  Premises  are  Comparisons  of  Inequality, 
comparisons  of  and  of  opposite  intensity,  they  must  be  read 
inequality.  pqe  gq  or  3d  Figure  ; thus, 

1st,  M>P,  and  4th,  P :>M, 

S cM,  _ M<S, 

offend  alike  against  the  Third  Axiom. 


m.] 


OF  SYLLOGISMS. SECT.  X. 


155 


But  2d,  M > P,  and  3d,  P > M, 

M<S,  S<M, 

.-.  S >P,  .-.  S<P. 

603.  We  have  seen  that  the  Indefinite  Comparisons 
cannot  be  converted,  and  must  always  be  indefinite  pre- 
regarded  as  Comparisons  of  greater  intensity,  mises- 
though  it  is  very  possible  in  any  case  that  they  are  not 
so.  Hence  when  such  a Comparison  occurs  in  such  a 
place  as  not  to  fulfil  the  conditions  of  Figures  just 
stated,  we  are  obliged  to  regard  the  Conclusion  as  in- 
valid ; thus,  M :>  P, 

S -f — M, 

.•.  S :>P  is  valid. 


But  M<P, 

S H — M gives  no  Conclusion,  as  the  compari- 
sons cannot  he  read  so  as  to  bring  them  under  the 
Axiom  of  Inequality.  We  might  indeed  read  thus  : 


P>M. 
S +-  M, 


or 


P 
S = 


M, 

M 


but  that  would  not  improve  the  matter  at  all  so  far  as 
their  conclusive  force  is  concerned,  for  we  could  not 
determine  the  comparison  between  S and  P. 

604.  When  but  one  Premise  is  a Comparative  Judg- 
ment the  Comparative  may  be  regarded  as  a 
Modal,  and  we  may  proceed  as  in  pure  cate- 
goricals ; thus, 

A is  greater  than  B, 

C is  A, 

C is  greater  than  B. 


One  Premise 
only  Compara- 
tive. 


H.  Comparative  Syllogisms  in  which  the  intensity  as  a 
difference  of  intensity  is  regarded  as  a cause.  a"3e’ 

605.  As  an  instance  take  the  following  from  Kos- 
suth’s late  speech  in  England  on  the  War  in  the  East : 
“ Kapoleon  failed  to  conquer  Russia  ; 

But  Hapoleon  was  superior  to  the  Allied  Powers  : 
Therefore  the  Allied  Powers  will  fail  to  conquer 
Russia  ” (that  is,  if  they  pursue  their  present  policy). 

In  this  case  we  have  a Comparative  Judgment  for 


156 


LOGIC. PAKT  I. 


[chap 


the  Minor  Premise,  in  which  the  Minor  and  the  Mid- 
dle terms  are  compared  with  reference  to  the  intensity 
of  some  property  which  they  have  in  common.  In  this 
case  it  is  “ military  force”  But  the  Major  term  here 
conclusion  af-  is  predicated  of  the  Minor  in  the  Conclusion, 
ground  of  sufif-  not  on  the  ground  of  any  of  the  Dicta  of  the 
oient  cause.  Figures,  hut  because  the  property  common 
to  both  of  the  terms  of  the  Comparative  Judgment  is 
conceived  to  be  the  cause  or  reason  why  the  Major 
term  is  predicated  of  the  Middle  in  the  Major  Premise, 
and  therefore  the  reason  why  it  may  he  predicated  of 
the  Minor  in  the  Conclusion.  But  this  implies  the  ex- 
istence of  that  which  is  the  cause  of  the  Major  term  in 
the  Minor  also,  and  moreoArer  that  it  exists  in  as  great 
intensity  at  the  least  in  the  Minor  term  as  in  the  Mid- 
dle. And  this  is  affirmed  by  the  Comparative  Judg- 
ment which  is  the  Minor  Premise. 

606.  In  Syllogisms  of  this  class  the  difference  in 
intensity  must  be  a real  Cause,  and  one  which  neces- 
sarily implies  the  reality  of  the  effect. 

ma”?earrisoumef  HI.  The  Comparatives  of  manner , time , 
place,  &c.  place,  ratio,  dec. 

607.  These  are  all  very  simple,  and  are  completed 
by  expanding  or  explaining  the  Comparative  Modal 
for  the  Minor  Premise  ; thus, 

The  Boys  are  with  their  Father  ; 

Their  Father  is  in  the  city  : 

The  Boys  are  in  the  city. 

A is  to  B as  C is  to  D, 

But  A is  one  half  of  B, 

.•.  C is  one  half  of  D ; 

or,  A is  to  B as  C is  to  D, 

But  A is  the  Father  of  B, 

.•.  C is  the  Father  of  D. 

608.  It  will  he  observed,  that  in  all  these  cases  the 
the* Major  Premie!  Comparative  is  the  Major  Premise. 


in.] 


OF  SYLLOGISMS. SECT.  XI. 


157 


609.  We  may  also  have  an  Indirect  Conclusion; 

thllS,  Indirect  Con- 

The  Boys  are  with  their  Bather  ; §a^«?§insy°“- 

The  Boys  are  in  the  city : g,sm3- 

The  Father  is  in  the  city. 

SECTION  XI. 

Of  Probable  Syllogisms. 

610.  By  the  application  of  Discrete  Quantity  to  the 
measure  of  Wholes  in  Continuous  and  Logical  Quan- 
tity, we  have  a further  modification  of  Formulae  and 
some  new  principles  and  rules  to  consider. 

611.  Arithmetic,  Algebra,  and  the  Calculus  are  hut 
methods  of  calculation  in  Discrete  Quantity.  CaIcu]ation9  in 
It  will  not  of  course  be  expected  that  we  Discrete  'S™ 
shall  go  into  a discussion  of  the  Rules  and  1 y' 
Formulae  belonging  to  these  Methods  in  this  place. 

612.  There  are  but  two  fundamental  Axioms  in 
Discrete  Quantity. 

(1.)  The  sum  of  the  parts  of  any  whole  is  that 

whole  itself.*  First  Axiom. 

The  usual  statement  that  the  sum  of  the  “ parts  is 
equal  to  the  whole,”  though  true,  belongs  to  Continu- 
ous rather  than  to  Discrete  Quantity. 

(2.)  If  from  any  whole  a part  he  taken,  the  remain- 
der is  such  a part  as  that  together  with  that  second  Axiom, 
which  was  taken  from  the  whole,  it  will  make  the  whole 
itself. 


* We  do  not  say,  “ equal  to  that  whole,”  for  that  would  imply  a want 
of  identity  in  the  terms  or  objects  of  the  conceptions.  We  say  that  “ a whole 
is  equal  to  the  sum  of  its  parts”  in  Continuous  Quantity,  Geometry,  &c. 
But  in  Arithmetic  we  say,  “ 3 times  4 is  twelve,”  not . “ is  equal  to  twelve.” 
Units,  as  such,  have  no  differentia — -and  sums  or  wholes  differ  only  in  the 
number  of  units  which  they  contain. 

When,  however,  in  Algebra  and  the  Calculus,  we  use  the  sign  of  equality, 
and  read  our  statements  or  Logical  Propositions,  “ X is  equal  to  A,”  it  is 
because  “ X ” and  “ A ” stand  for  quantities  which  while  they  are  equal  to 
each  other  as  quantities  have  other  relations,  which  must  he  kept  distinctly 
before  the  mind. 


158 


LOGIC. PAST  I.  [CHAP. 

The  first  is  the  Axiom  of  Addition , and  the  last 
that  of  Subtraction. 

613.  Where  several  equal  parts  are  to  be  added 
together  to  make  one  whole,  the  shorter  method  of 
Multiplication  is  adopted,  and  when  several  equal 
parts  are  to  be  taken  from  any  whole  the  method  used 
is  called  Division. 

614.  The  Involution  and  Evolution  of  Roots,  the 
Methods  in  Binomial  Theorem,  Fractions,  Indeterminate 

calculation.  Quantities,  Logarithms,  are  all  but  short  and 
convenient  ways  of  finding  values. 

But  it  is  important  for  us  to  investigate  in  this  place 
the  effect  of  the  application  of  Discrete  Quantity  to 
Logical  and  Continuous  Quantity. 

615.  By  introducing  Discrete  Quantity  a Compara- 
Discrete  Quan-  tive  Syllogism  which  offends  against  the 
Continuous.  Third  Axiom,  by  having  the  two  extremes 
either  both  greater  or  both  less  than  the  Middle  term, 
and  which  consequently  can  have  no  conclusion  by  a 
comparison  of  Continuous  Quantity  alone,  comes  to 
have  a valid  conclusion  ; thus, 

Three  is  two  less  than  five, 

Two  is  three  less  than  five, 

.*.  Two  is  one  less  than  three. 

616.  Again,  we  may  have  an  application  of  Dis- 
crete Quantity  to  Propositions  which  are  protensively 

ToProtensive  quantified,  so  as  to  give  a valid  conclusion 
Quantity.  one  that  oan  pave  none  without  it ; thus, 

0 The  cars  stop  at  W aterloo  one  half  of  the  time  ; 

The  cars  carry  the  mail  three  fourths  of  the  time  : 
Some  mail  trains  stop  at  Waterloo. 

617.  The  principle  involved  here  is  the  same  as 
to  Logical  that  which  controls  the  influence  of  Discrete 

Quantity  m ge-  Quantity  w}ien  applied  to  Logical  Quantity 

in  general.  For  example  take  the  following: — At  a 
certain  extensive  conflagration  it  is  ascertained  that, 
Three  fourths  of  the  buildings  in  a city  were  of  brick ; 
One  half  of  the  buildings  were  destroyed : 

.•.  Some  brick  buildings  were  destroyed. 


m.] 


OF  SYLLOGISMS. SECT.  XI. 


159 


618.  When  one  of  the  Extremes  is  expressed  in 

integral  Discrete  Quantity,  it  does  not  at  all  Extremeg  in 
modify  the  Formula,  as  in  the  following  ex-  auan" 

amples : 

All  that  were  in  the  Ark  with  Noah  were  saved ; 

Eight  human  beings  were  in  the  Ark  with  Noah  : 
.•.  Eight  human  beings  were  saved. 

All  terms  in  which  Discrete  Quantity  is  expressed 
by  the  numerals,  indicating  simply  how  many  are  in- 
cluded in  the  terms  are  undistributed.  Abso- 
lute Whole  belongs  to  Logical  Quantity,  and  disSbutld"01 
it  is  a Whole  which  is  not  included  as  an  alter- 
nate genus  in  any  more  comprehensive  Whole  or  Sphere. 
Infinite  belongs  to  Continuous  Quantity,  such  as  GOD, 
Space,  Eternity,  &c.  But  in  Discrete  Quantity  we 
know  of  no  number  so  large  that  it  may  not  be  a part 
of  a larger  and  more  comprehensive  Whole,  therefore 
none  which  is  absolute ; and  of  none  so  large  that  it 
may  not  be  made  larger  by  addition,  and  therefore 
none  which  is  infinite.  The  Units  have  no  properties 
by  which  they  are  distinguished  as  Individuals,  or 
divided  into  Genera  and  Species.  It  is  true  that  “ one 
man  ” has  such  properties,  but  not  as  “ one?  It  is  only 
as  “ man  ” that  he  has  differentia  and  peculiarities. 
Hence  in  Discrete  Quantity  there  are  no  Logical 
Wholes. 

619,  Since  a term  expressive  of  Discrete  Quantity 
alone,  as  “ six,”  “ ten,”  “ fifteen,”  &c.,  can  never  be  a 
distributed  term,  such  a Middle  term  can 

i n , 5 i -yt  , If  the  Middle 

never  help  us  to  any  conclusion.  JN  or  yet  be  merely  Dis- 
can  any  term  measured  by  Discrete  Quan-  there  can  be  no 
tity  serve  as  a Middle  term,  unless  it  ex-  Conclusion- 
presses  the  ratio  of  the  number  expressed  to  the  Dis- 
crete Quantity  of  the  Logical  Whole  denoted  by  the 
term.  For  example : 

Three  men  got  on  the  cars  at  the  station  ; 

Three  men  were  killed  in  the  cars  : 

.-.  The  men  killed  in  the  cars  were  the  men  who  got 
on  at  the  station. 


160 


LOGIC. — PABT  I. 


[CHAP. 


620.  The  fallacy  is  obvious. — Nor  from  this  state- 
ment can  we  infer  any  thing  of  the  amount  of  the  pro- 
bability that  any  one  of  those  who  thus  got  on  were 
among  the  killed.  Nor  should  we  gain  any  thing  by 
using  a much  larger  number  for  the  Middle  term. 

621.  It  is  only,  therefore,  when  the  Discrete  Quan- 
tity expresses  the  ratio  of  those  included  within  the 

The  Middle  scope  of  the  judgment  to  the  number  of 
either aRatio or  individuals  included  in  the  Logical  Whole 
a Fraction.  denoted  by  the  term  which  this  Discrete 
Quantity  qualifies,  that  it  can  be  available  for  the  pur- 
poses of  deduction. 

622.  We  shall  greatly  facilitate  our  understanding 
of  the  principles  upon  which  the  conclusiveness  of  these 

Method  of  Syllogisms  depends,  by  resorting  to  Plouc- 
Notation.  quet’s  Method  of  Notation,  or  at  least  a 
modification  of  it.  Let  a line  be  drawn,  which  by  its 
length  will  indicate  the  unit  of  which  the  Middle  term 
is  a fraction,  and  another  directly  under  it,  in  each  case 
denoting  the  amount  of  the  fraction. 

623.  Thus  to  take  the  example  just  given,  let  us 
denote  the  whole  number  of  houses  by  a line,  and  then 

how  many  at  directly  under  it  two  lines  more — the  one 
least-  one  half  and  the  other  three  fourths  as  long. 

And  since  we  wish  to  know  whether  any,  and  if  so, 
the  least  part  of  the  Minor  term  that  is  necessarily  con- 
tained in  the  Major,  we  will  place  one  of  the  fractional 
lines  even  with  the  unit  line  at  one  end,  and  the  other 
at  the  other  ; thus, 

i i i i I whole  number ; 

i i i | number  of  brick  houses ; 

i i i number  of  houses  burnt. 

624.  The  reason  for  placing  the  lines  as  above,  will 
be  obvious  from  the  fact  that  for  aught  that  appears 
to  the  contrary  in  our  statement,  all  of  the  not-brick 
houses  were  burnt,  and  only  so  many  of  the  brick 
houses  burnt  as  are  necessary  to  make  up  the  one  half ; 
that  is,  that  the  two  spheres  “ burnt and  “ brick” 


OF  SYLLOGISMS. SECT.  XI. 


161 


HI.] 

are  as  far  as  possible  opposite.  Hence  tbe  distance  by 
which  the  lower  line  overlaps  the  one  above  it,  will  he 
the  least  part  of  the  Minor  term  “ burnt ,”  which  can 
possibly  be  included  in  the  Major  term  “brick.” 

But  the  overlapping  portion  of  the  two  lines  is  one 
third  of  the  one  and  one  half  of  the  other. 

625.  Assuming  then  the  term  “ brick  houses  ” for 
the  Minor  term,  we  have  for  conclusion  : 

“ One  third \ at  least,  of  the  brick  houses  were 
burnt.” 

Or  taking  “ burnt  ” for  the  Minor  term,  we  have  : 

“ One  half,  at  least,  of  the  burnt  houses  were  brick.” 

626.  But  if  the  two  lines  when  thus  placed  did  not 
overlap  each  other  at  all,  there  would  be  no  assertive 
conclusion ; that  is,  we  could  not  say  positively  that 
any  of  the  burnt  houses  were  brick,  or  that  any  of  the 
brick  houses  were  burnt. 

627.  From  the  foregoing  it  is  certain  that  unless 

the  sum  of  the  two  fractional  values  used  as  Surp  of  the 
Middle  term  is  more  than  a unit,  we  have  hfmore t“na 
no  conclusion.  Unit- 

628.  The  Conclusion  in  these  cases  may  he  mea- 
sured in  Discrete  Quantity,  giving  the  pre-  conclusion  dis- 
cise  number,  which  is  the  least  that  can  fiedey  quant1' 
have  been  included  in  the  Predicate  of  the  Conclusion 
as  above,  or  we  may  have  the  undistributed  Subject  in 
Logical  Quantity,  “ Some  brick  houses  were  burnt.” 

629.  Or  if  we  place  the  lines  differently,  we  shall 

see  how  many  at  most  could  have  been  Howmanyat 
burnt.  most- 

i i i i i whole  number ; 

1 i i i brick ; 

1 i > burnt. 

630.  We  place  the  lines  thus  because  it  is  possible 
that  the  two  spheres,  “ burnt  ” and  “ brick,”  are  co- 
incident to  the  extent  of  the  comprehensiveness  of  the 
narrowest. 

631.  From  this  it  appears  that  if  the  Minor  term 


LOGIC. — PART  I. 


162 


[chap. 


lias  a sphere  less  comprehensive  than  the  Major  it  may 
be  wholly  included  in  it. 

632.  Let  us  now  pass  on  to  consider  the  application 
of  Discrete  Quantity  to  the  calculation  of  probabilities 
in  Syllogisms. 

633.  There  are  three  distinct  classes  of  cases  in  the 
Calculation  of  Probabilities,  which  we  will  consider  as 
involving  all  the  Logical  Principles  which  belong  to 
that  interesting  but  intricate  and  complicated  sub- 
ject. 

634.  (1.)  We  will  first  consider  the  effect  of  Dis- 
crete Quantification,  expressed  in  a ratio  or  a fraction 

one  probable  of  the  units  of  the  Middle  term,  when  one 
premise.  premise  only  is  a fraction  and  the  other  is 
unity ; thus, 

All  the  houses  in  the  city  were  brick  ; 

One  half  the  houses  were  burnt : 

.•.  All  the  burnt  houses  were  brick;  — or  con- 
versely, One  half  the  brick  houses  were  burnt. 

And  the  quantity  of  the  Conclusion  will  be  the  same 
Quantification  as  that  of  the  Major  Premise,  as  in  the  above 
ofthc  conciu  examp|eg_  The  £W0  Conclusions  from  the 

first  of  these,  as  will  be  seen,  results  from  our  regard- 
ing the  one  Premise  as  Major  in  the  one  case,  and  the 
other  in  the  other. 

635.  (2.)  The  next  class  of  cases  are  those  in  which 
Dependent  the  Premises  are  all  probable,  and  several 

probabilities,  probabilities  are  dependent  upon  each  other. 

636.  Of  these  we  have  two  kinds — ( a ) that  in  which 
we  have  several  Premises,  and  the  value  of  each  is 
expressed  in  fractions  of  the  common  Middle  term, 
as  in  the  case  j ust  given  : 

Three  fourths  of  the  houses  were  brick, 

One  half  of  the  houses  were  burnt ; 
and  (b)  that  kind  in  which  the  value  of  each  Premise 
(after  the  first)  is  expressed  in  fractions  of  the  value  of 
the  preceding  Premise. 

637.  (a)  The  probability  that  any  particular  house 
is  brick,  when  three  fourths  of  the  whole  are  brick,  is  of 


OF  SYLLOGISMS. SECT.  XI. 


163 


ni.] 


course  three  fourths.  And  the  probability  that  any  par- 
ticular house  is  burnt,  when  one  half  of  the 
whole  are  burnt,  is  ot  course  one  halt  or  the  |fJnon  i."  Frac- 
whole.  As  the  number  of  houses  that  are  S"  Middle 
of  brick,  and  the  number  that  are  burnt  are 
each  of  them  separately  less  than  the  whole,  the  pro- 
bability that  a brick  house  is  burnt,  or  that  a burnt 
house  is  brick,  is  of  course  less  than  the  probability 
that  any  particular  house  is  either  brick — or  burnt ; 
that  is,  the  probability  that  any  particular  house  is  both 
brick  and  burnt,  is  less  than  that  it  is  either  separately. 

638.  "We  have  seen  that  the  probability  that  any 
particular  house  was  burnt,  when  one  half  were  burnt, 
is  one  half  of  the  whole.  Now  of  course  the  probabi- 
lity that  any  burnt  house  was  brick,  is  one  half  of  the 
whole  number  of  the  brick  houses.  But  the  whole 
number  of  brick  houses  is  three  fourths  of  the  whole, 
the  probability  therefore  that  a brick  house  was  burnt 
is  one  half  of  three  fourths,  which  is  three  eighths  of 
the  whole  number  of  houses. 

639.  The  probability  that  any  particular  The  probabi- 

1 • i i -I  , • r*  ji  lity  of  any  one 

brick  nouse  was  burnt,  is  ot  course  the  same  chance  the  same 
as  the  number  ot  brick  houses  that  were  number  of  fa- 

-i  i , vorable  chan* 

probably  burnt.  ces. 

This  results  from  the  principles  laid  down  concern- 
ing the  effect  of  classification  upon  predication ; for 
each  brick  house  is  an  individual,  of  which  the  brick 
houses  burnt  is  the  species.  Hence  Avhatever  we  may 
predicate  of  the  individuals  distributively,  we  may 
predicate  of  the  species  generally,  and  vice  versa  what- 
ever we  may  predicate  of  the  species  we  may  predicate 
of  each  individual. 

Or  the  point  may  be  proved  in  another  way,  as 
follows  : 

640.  The  probability  that  any  one  house  was  burnt, 
is  the  same  as  the  probability  that  any  other  house 
was  burnt ; so  likewise  the  improbability.  p d mathe. 
The  probability  that  any  house  was  brick,  matically- 

is  as  we  have  seen  3 : 1,  three  to  one  : again  the  pro- 


164 


LOGIC. — PART  I. 


[CHAP. 


bability  that  any  one  house  was  burnt  is  1 : 1,  one  to 
one  against  it — that  is,  one  half.  Now  that  fraction 
which  sustains  the  same  ratio  to  the  number  of  brick 
buildings  in  the  city  that  the  number  of  the  burnt  does 
to  the  whole  is  f ; thus  | : 1 : : f : £■ — three  eighths  of 
the  whole  therefore  must  be  the  number  of  brick  build- 
ings that  were  probably  burnt.  And  if  more  than 
three  eighths  of  the  whole  number  were  burnt  from 
among  the  brick  buildings,  then  it  would  follow  that 
since  a larger  proportion  of  brick  than  of  the  non-brick 
were  burnt,  the  probability  of  any  particular  brick 
houses  having  been  burnt  is  greater  than  the  probabi- 
lity that  a non-prick  house  was  burnt. 

641.  ( b ) In  the  second  class  of  cases  we  have  suc- 
cessive Premises,  in  which  the  value  of  each  is  ex- 
pressed in  fractional  values  of  the  preceding  Premise, 
as  a whole  or  unity. 

This  Process  implies  the  form  of  the  Sorites  already 
explained  (554),  in  which  each  successive  judgment 
expressed  as  a single  cognition,  becomes  the  subject  to 
the  one  which  follows. 

642.  Thus,  suppose  that  a battle  has  been  fought, 
concerning  which  we  have  the  following  particulars  : 

Ratio  of  cai-  “ Three  fourths  of  the  men  in  the  army  were 

One  tenth  of  the  men 
miss- 


fhiatratnioYshm  hi  the  engagement. 
preceding0 rre^  that  were  engaged  in  the  battle  were 
mise.  illg.  f-]ie  nex(.  morning1,  and  one  third  of  the 


_ 'to? 

missing  were  killed.”  What  is  the  probability  that 
any  particular  man  was  killed  ? 

643.  It  is  obvious  that  | of  TV  of  those  engaged 
were  slain.  But  “those  engaged”  were  only  three 
fourths  of  the  rvliole.  Hence  £ of  | of  TV  that  T§„  = — 
were  slain. 

644.  And  from  the  reasoning  already  given,  the 
probability  that  any  particular  man  was  slain  on  the 
mere  general  ground  of  probability,  is  or  1 : 39. 

645.  If,  however,  we  have  any  particular  class  of 
special  grounds  men  among  whom  the  individual  concerning 

of  Probability.  ° . -i  -i  , • • • ° 

whom  we  are  making  our  calculation  is  in- 


ni.J 


OF  SYLLOGISMS. SECT.  XI. 


165 


eluded,  and  they  are  known  to  have  been  especially 
exposed,  the  probability  of  his  being  among  the  killed 
is  rendered  greater  by  the  consideration  of  that  parti- 
cular ground  affecting  the  amount  of  the  probability. 

• 646.  (3.)  We  will  next  consider  the  several  cases 
of  independent  probabilities : 

{a)  We  have  a class  of  cases  in  which  we  have  a 
probability  in  one  Premise,  and  an  improba-  Probability  and 
bility  in  another.  In  that  case  we  have  only  cSmb?ned.“ 7 
to  subtract  the  one  from  the  other,  and  the  remainder 
will  be  of  the  same  kind  as  the  largest  Premise. 

647.  But  when  we  have  a special  improbability 
against  an  event  to  be  combined  with  several  proba- 
bilities in  its  favor,  this  special  improbability  must  be 
computed  by  using  its  complement  as  a new  proba- 
bility, to  be  multiplied  in  according  to  the  principle  in 
the  last  named  class  of  cases. 

648.  Suppose  an  individual  to  have  belonged  to  a 
department  of  the  army  which  is  but  slightly  General  Proba. 
exposed,  call  this  an  improbability  of  f,  then  ciaitytmproblpbT- 
the  probability  that  one  in  that  department  lity- 

will  be  among  the  killed,  will  be  of  course  but  just 
of  the  probability  resulting  from  the  other  probabili- 
ties X o'  X j ■ j jo  ■ 

( b ) We  will  next  consider  the  class  of  cases  in 
which  the  question  is  of  one  of  several  One  of  several 

7 • /7  , ° chances  in  the 

chances  in  the  same  event . same  event. 

649.  Thus,  the  die  has  six  sides,  and  therefore  six 
chances  for  each  throw,  and  each  throw  is  an  event  in 
which  there  are  chances. 

650.  How  what  is  the  probability  that  either  of  two, 
say  the  ace  and  the  deuce , will  turn  up  in  any  Ratio  of  the 
single  throw  or  event  ? It  is  of  course  dou-  Calculation- 
ble  the  probability  of  any  one  side  or  chance  } + £ =|. 

651.  This  is  easily  proved  by  supposing  the  question 

to  be,  what  is  the  probability  that  some  one  Proved 
of  the  six  sides  will  fall  up.  By  the  rule  + •§-  + £+ 

| = | = 1 or  certainty. 

652.  But  we  know  previous  to  any  computation,  that 
one  of  the  six  sides  will  fall  uppermost  at  each  throw. 


166 


LOGIC. — PAJ3T  I. 


[chap. 


653.  Hence  in  all  cases  where  we  have  to  inquire 
what  is  the  probability  of  some  one  of  several  chances 
in  the  same  event,  we  may  add  the  sum  of  probabili- 
ties of  the  several  chances. 

654.  These  “ several  ” must,  however,  be  a part 
several  must  of  some  one  whole,  or  totality  of  chances,  as 

same  whole,  occurring  in  one  event,  otherwise  their  sum 
may  amount  to  more  than  unity  ; which  is  impossible. 
Thus,  suppose  we  have  three  probabilities,  not  included 
in  any  such  unity,  they  may  be  |,  i,  i,  then  l+y  + |=r| 
which  is  absurd. 

655.  ( d ) This  brings  us  to  the  last  class  of  cases 
One  chance  in  which  we  will  consider — namely,  that  in 

several  events.  i • i ,•  • l 

which  the  question  is  concerning  one  chance 
in  several  events. 

656.  Of  these  there  are  two  kinds — ( d 1st)  where  the 
two  kinds.  events  are  in  the  same  totality  of  chances  ; 
and  ( d 2d)  where  they  are  in  ditferent  totalities. 

657.  ( d 1st)  For  the  simplest  case  in  this  kind,  sup- 
Differentia  ot  Pose  we  have  the  question,  “ What  is  the  pro- 
the  erst.  bability  of  throwing  any  particular  number 
on  a die  in  two  different  throws  ? ” 

658.  The  probability  of  its  being  up  in  the  first 
throw  or  event  is  } , and  the  independent  probability 
of  its  being  up  in  the  second  throw  or  event  is  also  } . 

659.  Here  the  totality — the  six  sides  of  the  die — is 
the  same  in  both  cases,  the  two  throws  are  different 
events. 

660.  ( d 2d)  But  for  a case  of  the  second  kind  take 
the  following : 

Two  thirds  of  the  pious  are  grave  persons. 

Three  fourths  of  the  studious  are  grave  persons. 
Here  the  different  totalities  are  “ the  pious  ” and 
Differentia  of  “ the  studious,”  and  the  question  is  what  is 
the  second.  the  probability  that  one  who  is  both-  “ pious  ” 
and  “ studious  ” will  be  “ grave.” 

661.  The  principle  or  rule  of  calculation  is  the 
same  in  both  of  these  varieties  of  this  class  of  cases. 

662.  And  we  have  two  distinct  questions  to  con- 


OF  SYLLOGISMS. — SECT.  XI. 


167 


in.] 

sider — (1)  What  will  be  the  average  of  the  probability 
of  one  chance  in  any  given  number  of  events  ? The  two  Ques. 
and  (2)  What  is  that  probability  in  any  par-  tions- 
ticular  case  ? 

663.  These  questions  are  by  no  means  the  same. 
In  any  indefinitely  large  number  of  events,  By  no  mean3 
it  is  evident  that  each  side  would  he  upper-  the  same- 
most — that  is,  each  chance  would  happen  just  as  often 
as  any  other  one  chance.  Each  side  of  the  die  there- 
fore would  come  up  just  one  sixth  of  the  whole  num- 
ber of  events.  If  now  we  divide  this  totality  of  events 
into  pairs,  then  of  course  a given  side  would  come 
uppermost  just  as  often  as  before  ; that  is,  1 : 5 in  the 
whole.  But  the  probability  of  any  given 
side  coming  up  once  m every  pair  ot  events,  iating  the  aver- 

ox.  i ii  age  probability. 

on  an  average  is  one  tiiircL  as  great  as  the 
probabilitjr  of  its  coming  up  once  in  three  times  as 
many  chances,  or  twice  as  great  as  that  of  its  coming 
up  in  each  chance  ; that  is,  So  if  we  divide 

the  events  into  triplets,  the  probability  of  any  given 
side  on  the  average  of  an  immense  number  of  events 
is  three  times  as  great  as  in  the  single  event,  that  is, 

L 4-1-4--  = — 

6*6*6  2 * 

661.  How  in  this  way  the  fraction  can  amount  to 
more  than  unity,  for  as  there  are  but  six  sides 

-i  • r»  it..,!  -i  The  result  may 

or  chances,  so  11  we  ask  what  is  the  proba-  be  more  than 
bility  of  ace,  for  instance,  in  sets  of  ten  ums' 
events,  we  have  j taken  ten  times  orl;  that  is,  ace 
will  come  up  on  an  average  more  than  once  in  every 
ten  throws.  Otherwise  ace  will  not  come  up  so 
often  as  some  of  the  other  sides.  But  if  it  does  not 
then  there  is  some  special  reason  or  ground  of  proba- 
bility, which  is  contrary  to  the  supposition  on  which 
we  started. 

Let  us  now  consider  the  other  question — what  is 
the  probability  of  any  particular  chance  in  a definite 
number  of  events. 

665.  It  certainly  can  make,  no  difference  whether 
the  events  are  in  the  same  totality  of  chances  or  not, 


168 


LOGIC. — PART  I. 


[CHAP. 


since  in  the  throw  of  the  die,  for  instance,  the  probabi- 
immateriai  anJ  Particular  side  in  each  throw  is 

whether  the  certainly  iust  as  independent  of  each  and 

events  be  in  f.  . ~ 

ityornot6  total'  eveiT  other  throw,  as  it  is  ot  the  probability 
of  the  head  side  of  a cent’s  coming  up  in  any 
throw  of  the  cent. 

666.  We  may  therefore  consider  the  two  kinds  of 
cases  in  the  class  which  we  have  named  above  {d),  as 
depending  upon  the  same  principle  and  requiring  to 
be  calculated  by  the  same  rule. 

Now  we  have  two  conditions  to  fulfil : 

667.  (1.)  The  probability  of  any  chance  in  two  events 
Twocondiuons  must  be  greater  than  it  is  in  either  one  of 

ist  condition,  them  alone  ; thus  the  probability  of  the  ace 
in  two  throws  is  greater  than  it  is  in  one. 

668.  And  not  only  so,  but  the  probability  in  any 
number  of  combined  throws  must  be  greater  than  that 
of  the  sum  of  all  the  throws  excepting  any  one  of 
them  ; that  is,  two  must  be  greater  than  any  one  in 
the  two,  three  than  any  two  in  the  three,  four  must  be 
greater  than  any  three  in  the  four,  and  so  on. 

669.  (2.)  The  sum  of  the  combined  probability  can 
2d  condition,  never  amount  to  any  more  than  unity — for 
by  the  very  mode  of  reckoning  probabilities  they  are  but 
the  fractions  of  unity.  When  therefore  they  amount  to 
unity,  they  are  no  longer  probabilities  but  a certainty, 
and  there  can  be  nothing  beyond. 

670.  Now  in  the  case  of  the  die,  for  instance,  as 
there  are  six  sides  the  probability  of  throwing  any 
we  cannot  add  particular  side,  say  the  ace,  at  the  first  throw 
the  fractions.  would  be  1 1 5.  or  }.  And  in  six  throws  it 
would  be  |+j+i  + H-j+£  or  £x6=l  unity.  And  yet 
it  is  possible  that  the  given  side  might  not  be  thrown 
once  in  six  times,  or  even  in  any  greater  number.  There 
is  a bare  possibility  that  that  side  might  not  fall  upper- 
most in  a thousand  times.  Still,  however,  when  the 
And  yet  cannot  event  is  far  from  the  sum  of  the  probabilities 
nlehum  ofThe  (provided  they  keep  within  unity)  in  either 
probabilities,  direction — that  is,  greater  or  less  ; it  creates 


in.] 


OF  SYLLOGISMS. — SECT.  XI. 


169 


a presumption  and  finally  the  unhesitating  belief  that 
there  is  some  special  cause  influencing  the  chances,  as 
that  a die  is  loaded. 

671.  It  appears  therefore  that  we  cannot  calculate 
the  probability  by  adding  the  value  of  each  fraction, 
since  that  method  would  soon  produce  unity,  and  ex- 
ceed it  even. 

672.  Nor  can  we  calculate  it  by  multiplying  the 
fractions.  The  value  in  each  successive  Pre-  we  ] cannot 
mise  is  not  a fraction  of  that  of  the  preced-  Fractions.  e 
ing  or  of  any  other  fraction.  Each  one  is  the  fraction 
of  a unity,  and  of  a different  unity,  as  the  1st  and  2d 
throws  in  the  first  example,  and  “ the  pious,”  and  “ the 
studious  ” in  the  second.  And  besides  the  multipli- 
cation of  the  fractions  would  give  us  a constantly  de- 
creasing probability,  when  obviously  we  ought  to  have 
an  increasing  one. 

673.  If  now  instead  of  the  probability  in  each  Pre- 
mise we  take  its  complement  improbability,  By  means  of 
and  multiply  them  together  as  fractions,  and  my. lmprobd  1 
then  take  the  complement  of  that  product  for  the  pro- 
bability of  the  conclusion,  we  shall  have  a method 
answering  exactly  the  demands  of  the  case. 

671.  Thus  in  the  first  case  the  probability  of  an  ace 
in  two  throws  is  £ and  £,  the  complement  is  £ and  £, 
multiplying  we  have  ff , and  taking  the  complement 
we  have  ££.  In  five  throws  it  becomes  ££££,  in  six 
!£!££,  thus  approaching  but  never  reaching  unity  or 
absolute  certainty.* 


* For  the  gratification  of  those  who  would  like  to  see  this  in  a more 
purely  mathematical  form  I give  the  following  demonstration. 

Let  the  probability  of  a particular  chance  in  one  event  be  and  that 

b 

of  the  same  chance  in  another  event  f , certainty  being  unity.  The  com- 
bined probabilities  can  never  be  greater  than  unity,  nor  less  than  the  sum 
of  all  minus  any  one  of  them. 

Now  multiply  the  complement  of  A which  is  (1  — f)  by  the  complement 


no 


LOGIC. — PART  I. 


[chap. 


675.  In  the  second  case  we  have  f,  or  t comple- 
ment in  unity,  and  £ , or  f complement.  Multiplying, 
we  have  = T\-  or  probability  that  the  man  who 
is  both  “ studious  ” and  “ pious  ” is  “ grave.”  * 


SECTION  XII. 

Of  Conditional  Syllogisms. 

676.  We  are  not  to  consider  all  sentences  stated  in 
the  conditional  form  as  expressing  a conditional  judg- 


of  — which  is  (1  ■ 
a 


-)  and  we  have 

a 


■( b—a ) (d  — c) 

Vd 


as  the  comple- 


ment of  the  product,  which  is  the  combined  probability.  For  as  the  nume- 
rator cannot  be  greater  than  bd , the  fraction  itself  can  never  exceed 
unity. 


Again  this  fraction  may  he  put  under  the  form  -4-  (I  — f a quan- 

b b d 


tity  which  can  never  be  less  than 


a 

b' 


Now  suppose  that  both  independent  probabilities  are  unity,  then  they 
are  not  probabilities ; they  have  no  complements  and  so  of  course  they 
cannot  be  multiplied. 

Again,  suppose  them  to  be  indefinitely  near  to  unity,  then  applying 
the  doctrine  of  limits,  they  may  be  assumed  as  unity,  and  so  will  have 
no  complements  to  be  multiplied. 

In  either  case  the  fraction  becomes  — - or  unity,  that  is  1 x 1 = 1. 

bd 

But  suppose  the  probability  in  each  case  to  be  as  near  to  unity  as  the 
nearest  assignable  quantity,  then  by  this  rule  the  product  of  two  such  pro- 
babilities would  be  nearer  than  any  assignable  quantity  or  indefinitely  near. 
We  may  pursue  the  demonstration  in  this  way  for  every  assignable  value  to 
the  fraction.  If  therefore  there  is  any  other  rule  that  will  give  the  same 
result,  it  is  not  another  but  the  same.  But  if  it  gives  a different  result  it 
cannot  be  true. 

* I have  taken  no  notice  of  the  effect  of  concurrence  upon  the  probabili- 
ties ; this  will  be  considered  in  the  Chapter  on  Methods  of  Proof.  But  it 
will  often  happen  that  the  concurrence  of  two  very  small  probabilities  will 
produce  an  amount  of  conviction  but  very  little  if  any  short  of  certainty. 
Thus,  suppose  two  men  whose  veracity  was  nothing  should  come  in  and 
report  to  me  a certain  occurrence,  the  one  after  the  other,  and  under  such 
circumstances  that  I could  know  that  there  had  been  no  collusion  between 
them — the  strength  of  the  combined  testimony  might  be  but  very  slight — • 
but  the  fact  of  their  concurring  without  collusion  would  be  very  convincing, 
and  all  the  more  so,  the  more  strange  and  unexpected  the  event  whioh  they 
narrate. 


m.] 


OF  SYLLOGISMS. — SECT.  XII. 


171 


ment.  It  is  often  the  case  that  statements  are  made 
in  the  hypothetical  form  where  no  logical  Not  al,  Comii. 
dependence  of  one  member  upon  the  other  condkifnauSdy 
is  intended.  Thus,  “ If  on  the  one  hand  ments- 
Greece  failed  by  an  excess  of  the  popular  element  in 
its  constitution,  Rome  on  the  other  became  purely  a 
military  despotism,  the  least  favorable  of  all  forms  of 
government  to  popular  liberty.”  Here  manifestly 
the  judgment  concerning  Rome  is  not  intended  to  be 
made  dependent  upon  the  truth  of  that  concerning 
Greece.  We  must  regard  the  judgments  therefore  as 
being  logically  two  entirely  distinct  categorical  affirma- 
tions. 

677.  ISTor  is  it  always  the  case  where  a Proposition 
is  a Conditional  Judgment  that  the  deductive 


The  Conditi- 


force  depends  upon  the  peculiarities  of  the  anme?”M^li 
Conditional  Judgment.  pfremi?eatesoric 

As  examples  take  the  following  : 

Whatever  comes  from  God  is  entitled  to  faith  and 
obedience. 

If  the  Scriptures  are  not  an  imposture  they  came 
from  God. 

.'.  If  they  are  not  an  imposture  they  are  entitled  to 
faith  and  obedience. 

Or  thus  : All  Y is  X, 

(If  Mis  Z,  A)  is  Y, 

.•.  (If  M is  Z,  A)  is  X. 

678.  In  this  case  the  Conditional  is  merely  the  Mo- 
dal of  the  Minor  Term,  and  is  treated  accordingly. 
The  Premise  is  used  as  a Complex  Categorical  rather 
than  as  a Conditional. 

679.  But  when  the  Conditional  Judgment  conditional 
is  used  as  such,  it  is  the  Major  Premise,  and  jor  Premise  in 
there  are  two  ways  of  completing  the  For-  syllogisms, 
mula. 

From  the  nature  of  Conditional  Judgments  it  fol- 
lows that : 

(1.)  If  we  affirm  the  Antecedent  the  Consequent 
cannot  be  denied. 


172 


LOGIC. — PAST  I. 


[chap. 

(2.)  If  Ave  deny  the  Consequent  the  Antecedent 
must  be  false ; that  is,  the  contradictory  of  the  Ante- 
cedent must  be  true. 

680.  Hence  we  may  complete  in  what  is  called  the 
constructive  Constructive  Method,  or  modus  ponens,  by 

ml""/.  rL  affirming  the  Antecedent  for  a Minor  Pre- 
mise, and  have  the  Consequent  for  a Conclusion ; 
thus,  If  A is  B,  A is  C, 

But  A is  B, 

.-.  A is  C. 

681.  Or  secondly,  we  may  complete  the  Formula 
Destructive  in  the  Destructive  Method , or  modus  toilens ,* 
mise°r  re  by  using  the  contradictory  of  the  Consequent 
for  Minor  Premise,  and  then  we  shall  have  the  contra- 
dictory of  the  Antecedent  for  Conclusion  ; thus, 

If  A is  B,  C is  D, 

But  some  C is  not  D, 

.•.  Some  A is  not  B. 

682.  But  by  denying  the  Antecedent  in  simple 
conditionals  we  do  not  disprove  the  Consequent,  nor 
by  proving  the  Consequent  do  we  prove  the  Ante- 
cedent. 

683.  But  the  Conditional  Proposition  is  sometimes 
Fxninw  m n made  an  Exclusive  Conditional  by  the  inser- 
" tion  of  “ only,”  “ alone,”  &c. 

684.  The  effect  of  this  exclusive  is  to  show  that  the 
Consequent  can  have  no  other  Antecedent,  and  could 
not  exist  without  the  one  given  in  the  Conditional. 
Thus,  “ If  the  Trojans  came  into  Italy  contrary  to  the 
will  of  the  gods,  they  would  then  alone  have  deserved 
punishment. 

But  they  did  not  come  contrary  to  the  will  of  the 
gods. 

/.  They  do  not  deserve  punishment.” — Virg.  MJn. 
X.  31. 

* The  words  “ posit  ” and  “ amote  ” have  sometimes  been  used  to  ex- 
press these  processes.  Thus  if  we  posit  the  Antecedent  the  Consequent 
must  follow,  and  if  we  amote  the  Consequent  the  Antecedent  must  be 
false. 


m.] 


OF  SYLLOGISMS. — SECT.  XII. 


173 


685.  In  this  case  by  denying  the  Antecedent  we 
disprove  the  Consequent. 

And  if  we  affirm  the  Consequent  we  establish  the 
Antecedent. 

They  deserved  punishment ; 

.•.  They  came  into  Italy  contrary  to  the  will  of  the 
gods. 

686.  But  without  the  Exclusive  Modal  we  prove 

nothing  concerning  the  Consequent  by  dis-  no  conclusion 
provmg  tne  Antecedent.  site  Methods. 

687.  This  will  be  obvious  by  the  following  illustra- 
tion “ If  John  has  a fever  he  is  sick.”  ITence  if  we 
prove  the  Antecedent,  viz.,  that  “John  has  a fever,” 
the  Consequent  that  “ he  is  sick  ” will  not  be  denied. 
But  if  we  disprove  the  Antecedent  and  show  that  “ he 
has  not  a fever,”  we  have  not  proved  that  “ he  is  not 
sick.”  He  may  be  sick  from  some  other  disease. 

688.  For  the  same  reason,  though  operating  in  the 
inverse  order,  if  we  prove  the  Consequent  we  do  not 
thereby  prove  the  Antecedent ; that  is,  if  we  prove  that 
“John  is  sick,”  we  have  not  proved  that  “he  has  a 
fever ; ” his  ailment  may  be  something  else  for  aught 
that  would  need  to  appear  in  our  argument. 

689.  The  whole  force  of  Hypothetical  reasoning  in 
either  method  must  depend  upon  the  Se-  The  validity  of 
quence.  There  must  be  some  such  connection  dependsnclupon 
between  the  Consequent  and  the  Antecedent  the  Sequence- 
in  the  nature  of  things  and  independent  of  our  volition, 
that  the  truth  of  the  one  follows  from  that  of  the 
other. 

690.  But  as  we  have  already  considered  the  Se- 
quence or  ground  of  affirmation  in  Conditionals,  we 
need  not  add  any  thing  more  concerning  it  Any  Enthy. 
here  except  to  make  the  remark  that  the  “^“css“aycobnc 
Premise  of  any  Enthymeme  may  be  made  ditionally- 
an  Antecedent,  and  the  Conclusion  a Consequent  in  a 
Conditional  Judgment,  and  then  the  other  Premise  will 
be  the  sequence  ; thus,  If  M is  P,  S is  P. 

Completing  as  before  we  have  : 


174 


LOGIC. — PART  I. 


[CHAP. 


If  M is  P,  S is  P, 

But  M is  P, 

S is  P. 

691.  But  regarding  it  as  an  Entliymeme,  we  have  : 

M is  P, 

S is  M , 

.-.  S is  P. 

692.  In  the  same  way,  any  Conditional  by  means 
sequence  of  its  Sequence  is  converted  into  a Catego- 

ric“sme  Cate80‘  rical  Syllogism. 

693.  It  is  sometimes  the  case  that  the  Conclusion 
depends  rather  upon  some  modal  of  the  general  Se- 

Modified  se-  quence  than  upon  the  general  sequence  itself, 
quence.  Thus  if  I say,  “ If  John  has  a fever  he  will 
die,”  the  general  sequence  is  “ all  that  have  fevers 
die,”  which  is  non  verapro  vera  ; the  Sequence,  there- 
fore, if  there  be  one,  must  be  found  in  some  peculiarity 
of  “ John,”  to  be  expressed  by  a modal.  The  Sequence 
then  would  be,  “ All  ( sub  modo ) who  have  fevers  die  ; ” 
the  sub  modo  denoting  the  differentia  of  the  class  to 
which  the  subject  of  the  Antecedent  belongs.  This 
modal,  however,  should  always  be  stated  either  in  the 
Antecedent,  or  by  giving  the  Sequence  stated  in  such 
a form  as  to  clearly  point  it  out. 

694.  If  the  Conditional  has  four  distinct  terms,  of 
conditionals  course  the  Sequence  becomes  double,  and 

tel™.  our  the  Conditional  as  an  Entliymeme  is  com- 
pleted into  a Sorites.  Thus,  If  A is  B,  C is  D. 

And  we  complete  thus,  C is  A, 

A is  B, 

B is  D, 

.-.  C is  D. 

695.  In  what  is  called  the  Compound  Conditional, 
it  is  necessary  to  prove  all  the  Antecedents  in  order  to 

compound  establish  the  Consequent.  If,  however,  we 
conditionals,  disprove  the  Consequent,  we  show  that  some 
one  or  more  of  the  Antecedents  is  untrue,  without  de- 
termining by  the  Formula  which  it  is. 


in.] 


OF  SYLLOGISMS. SECT.  XHI. 


175 


696.  This  makes  the  Minor  Premise  a compound 
compulative  categoric  Proposition.  Thus, 


697.  In  continuous  Conditionals  if  we  prove  the 
first  Antecedent  all  the  rest  will  follow.  continuous 
Thus,  If  A is  B,  C is  D ; — If  C is  D,  E is  F ; — conditional,-. 
If  E is  F,  F is  H,  and  so  on ; since  each  Antecedent 
after  the  first  is  the  Consequent  of  the  preceding  Con- 
ditional, it  is  established  by  that  first  Antecedent. 

And  conversely,  if  we  disprove  the  last  Consequent 
we  have  disproved  all  the  Antecedents. 

698.  We  may  also  have  Conditionals  with  Disjunc- 
tive Consequents.  Thus,  “ If  grain  is  cheap  conditionals 
it  must  be  either  because  the  crops  are  large,  ^leh 

the  consumers  are  comparatively  few,  or  the  quenta- 
importations  are  extensive.” 

699.  Completing  this  Formula  and  we  have  a Dis- 
junctive Conclusion.  Thus, 

If  A is  B,  either  C is  D,  or  E is  F, 

But  A is  B, 

.*.  Either  C is  D,  or  E is  F. 

700.  But  if  we  complete  in  the  Destructive  Method, 
we  must  deny  all  the  members  of  the  Disjunctive  Con- 
sequent. Thus, 

If  A is  B,  either  C is  D,  or  E is  F, 

But  neither  is  C,  D,  nor  E,  F, 

.*.  Some  A is  not  B. 


701.  It  has  sometimes  been  held  that  there  are  two 
classes  of  Disjunctive  Judgments — the  Divi-  comprehensive 
sive  and  Comprehensive.  Those  which  we  Disjunctive1"™ 
have  already  considered  are  the  Comprehensive  Dis- 
junctive Judgments. 


But  A is  B,  and  C is  D, 


.*.  E is  F. 


SECTION  XIII. 

Of  Disjunctive  Syllogisms. 


176 


LOGIC. — PAET  I. 


[CHAP. 


702.  The  Divisives  are  rather  categorical  judg- 
arehratherr‘oves  ments>  in  which  the  divided  whole  is  one 
pound  catego-  term  and  the  coordinate  terms  are  the  other. 

Thus,  “ All  food  is  either  vegetable  or  ani- 
mal.” 

But  we  will  postpone  the  consideration  of  the  com- 
pletion of  the  Formula  of  this  class  until  we  have  at- 
tended to  the  other,  or  the  Comprehensive  Disjunctives. 

703.  AYe  have  already  examined  the  Disjunctive 
Judgments.  They  affirm  that  one  of  two  or  more 
judgments  contained  in  the  Disjunctive  Proposition 
must  be  true  without  at  all  indicating  which  that 
one  is. 

701.  But  it  is  not  always  the  case  that  the  deduc- 
Deduction  does  tion  depends  upon  this  opposition  of  the 

not  always  de-  I T.>  . -r-*  x 

pend  upon  the  parts,  when  a Distinctive  Proposition  occurs 

Excluded  Mid-  1 7 xi  J • mi  1 

die.  as  one  ot  the  Premises,  lhus, 

Every  conqueror  is  (either  a hero  or  a villain)  ; 
Csesar  was  a conqueror  : 

.•.  Csesar  was  (either  a hero  or  a villain). 

All  Y is  (either  X or  AY), 

All  Z is  Y, 

.•.  All  Z is  (either  X or  AY). 

Or  the  Disjunctive  may  be  the  Minor  : 

All  Y is  X, 

Either  (Z  or  AY)  is  Y, 

.•.  Either  (Z  or  AY)  is  X. 

Or  finally,  the  Middle  Term  may  be  Disjunctive  in 
one  of  the  Premises.  Thus, 

Gold,  silver,  and  platina  are  malleable  ; 

All  precious  metals,  are  either  gold,  silver,  or  pla- 
tina : 

.•.  All  precious  metals  are  malleable. 

705.  But  in  this  case  the  Disjunctive  Middle  must 
enumerate  all  the  coordinate  parts,  and  in  one  Premise 
at  least,  as  above,  it  must  not  appear  as  a Disjunctive. 

For  if  we  say — Either  gold,  or  silver,  or  platina 
Not  Disjunctive  is  malleable  — as  Major,  and  then  write 
miseiu  1 rc‘  the  Minor  as  above,  we  should  manifestly 


m.] 


OF  SYLLOGISMS. — SECT.  XIII. 


177 


have  an  undistributed  Middle  ; and  we  might  have  the 
following  as  all  the  truth  there  would  be  necessary  in 
the  Formula : 

Either  gold,  or  silver,  or  platina  is  malleable  ; 
(suppose  it  to  be  gold  only  that  is  malleable) : 

All  precious  mettils  are  either  gold,  silver,  or  platina ; 
(suppose  it  to  be  silver  and  platina  only  that  are  pre- 
cious metals),  and  then  manifestly  we  should  have  no 
Conclusion,  for  the  Major  term  was  compared  with 
gold  and  the  Minor  with  silver  and  platina.  This  is  in 
fact  what  is  always  done  in  the  fallacy  of  undistributed 
Middle. 

706.  In  all  the  above  examples  the  judgment  is  not 
Disjunctive.  It  is  merely  a compound  categorical 
judgment  with  a Disjunctive  for  either  subject  or  pre- 
dicate as  the  case  may  be. 

707.  We  have  seen  that  the  ground  of  a Disjunc- 
tive Judgment  properly  so  called,  that  is,  a Compre- 
hensive Disjunctive,  is  the  Excluded  Middle.  It  will 
follow,  therefore,  that  if  we  deny  one  of  the  members 
the  other  must  be  true. 

708.  Hence  in  all  Disjunctive  Syllogisms  the  Dis- 
junctive Judgment  is  the  Major  Premise.  Disjunctive 
For  the  Minor  we  have  the  Contradictory  of  Mafo?eplemte 
one  of  the  Members,  and  for  the  Conclusion  syii<^lsms.ctive 
the  other  Member.  Thus, 

Either  A is  B,  or  A is  C, 

But  A is  not  B, 

.\  A is  C. 


Or,  Either  A is  B,  or  A is  C, 
But  A is  not  C, 
.•.  A is  B. 


709.  This  is  called  by  the  Scholastic  writers  the 

modus  tollente  ponens.  “ tolleDte 

710.  But  if  the  coordinate  terms  are  also  coordinate 
parts  of  the  divided  whole,  and  not  merely  Modus  ponente 
Alternate  Species,  we  may  also  complete  in  tollens- 

the  modus  ponente  tollens. 

8* 


178 


LOGIC. PART  I. 


[CHAP. 


Thus  Either  A is  B,  or  A is  C, 
But  A is  B, 

.•.  A is  not  0. 


This  is  either  gold  or  platinum  ; 

It  is  platinum  : 

It  is  not  gold. 

The  validity  of  this  Conclusion  depends  not  upon 
The  mode  de-  the  simple  Excluded  Middle  but  upon  the 
vision.  Jaw  ot  .Division,  that  no  individual  can  be  m 
more  than  one  of  the  coordinate  parts  of  any  divided 
whole  at  the  same  time  and  in  the  same  respect. 

711.  When  there  are  more  than  two  members  we 
More  than  two  obtain  only  a compound  categorical  Propo- 
sition for  the  first  answer.  Thus, 

Either  A is  C,  or  A is  B,  or  A is  D, 

But  A is  not  C, 

.-.  Either  A is  B,  or  A is  D. 

We  may  thus  proceed  with  this  as  before,  and  then 
we  shall  get  a simple  categorical  Conclusion.  Thus, 
Either  A is  B,  or  C 
But  A is  not  B, 

.-.  C is  D. 


712.  From  the  foregoing  it  will  be  seen  that  what 
Divisive  Dis-  are  called  the  Divisive  Disjunctives,  can  be 
pie* :ed 'on i y^by  completed  by  a Discretive  Categorical  alone. 
Thus, 


Discretives. 


All  A is  either  B or  C, 

S is  A but  it  is  not  B, 

.-.  S is  C ; 

that  is,  we  must  include  the  Subject  of  the  Conclu- 
sion in  the  Subject  of  the  Major  Premise,  which  is  the 
divided  whole,  and  at  the  same  time  exclude  it  from 
all  the  parts  except  one,  which  one  is  predicated  of 
the  Subject  of  the  Conclusion. 

713.  ISTor  is  the  Method  materially  different  when 
the  divided  whole  is  the  Predicate  instead  of  the  Sub- 
ject in  the  Disjunctive.  As, 


m.] 


OF  SYLLOGISMS. SECT.  XIV. 


179 


a b and  c constitute  M, 

S is  M but  not  a, 

.*.  S is  either  b or  c. 

SECTION  XIV. 

Of  the  Dilemma. 

711.  The  Dilemma  seldom  needs  or  requires  any 
completion.  It  differs  from  the  Compound  Dilemma. 
Conditional  in  that  its  Antecedents  hear  such  a relation 
to  each  other  as  to  constitute  an  Excluded  Middle,  and 
therefore  some  one  of  them  must  be  true.  And  as  the 
Consequent  may  be  predicated  on  either  one  of  them 
alone,  it  is  immaterial  which  of  the  Antecedents  is 
denied,  as  its  denial  affirms  the  other. 

715.  These  Antecedents  are  sometimes  called  the 

horns  of  the  Dilemma.  Dilemmaof  the 

716.  The  Dilemma  is  often  Complex  by  having 
several  Antecedents  one  after  another. 

Thus  Demosthenes  says : 

“ If  iEschines  partook  in  the  public  rejoicing  he  is 
inconsistent. 

If  he  did  not  he  is  unpatriotic.” 

717.  But  in  all  such  cases  there  is  a real  Conse- 
quent in  which  all  the  Antecedents  or  series 

of  Antecedents  unite.  The  obvious  Conse-  to  the  Complex 
quent  in  the  above  case  is  that  therefore  iemma' 
“.kEschines  is  unworthy  of  public  favor  and  confidence.” 

The  Formula  may  be  thus  expressed  : 

If  A is  B,  A is  C,  But  If  A is  C, ) A • 

Or,  If  A is  B,  A is  D,  And  If  A is  D,  j ^ 1S 

718.  Hence  we  may  say,  “ Whoever  committed  this 
fault  is  either  too  ignorant  to  be  our  guide  or  too  dis- 
honest to  be  trusted — in  either  case  he  is  unworthy  of 
our  confidence.” 

Which  we  may  represent  thus  : 

If  A is  B,  A is  not  C,  And  If  A is  not  C,  ) A is  not 


180 


LOGIC. PART  I. 


[CHAP. 


719.  The  Dilemma  is  not  unfrequently  stated  in  an 
wiemma  stat-  inverted  form.  Thus,  If  A is  B,  either  A is 
ed form. invert  D,  or  A is  F.  “If  lie  fails,  it  is  because 
he  is  ignorant  of  his  profession  or  inattentive  to  his 
duties.” 

720.  This  may  be  regarded  as  an  Enthymeme 
stated  conditionally  with  a Disjunctive  Conclusion,  or 
a Major  Term  with  a Disjunctive  Modal  similar  to  the 
instance  already  given,  &c.  Thus, 

All  B is  either  D or  F, 

A is  B, 

.’.  A is  either  D or  F ; 

or  in  the  other  form,  Either  A is  D,  or  A is  F. 

721.  It  is  not  unfrequently  the  case  that  in  stating 
the  Dilemma,  the  Antecedents  are  alone  stated  in  dis- 
junctive opposition  to  each  other,  and  the  Formula  is 

The  con  e °*  course  nothing  more  than  a Disjunctive 
quent  some-  Judgment.  But  as  the  Consequent  of  the 
truth  ot  either  member  is  so  obvious,  and  is 
in  fact  suggested  by  the  circumstances  and  the  occa- 
sion, the  statement  is  considered  a Dilemma  never- 
theless. Tims,  “ The  Dilemma  then  presents  itself  to 
us  anew : Either  we  must  accept  the  doctrine  of  the 
transmutation  of  species  and  suppose  that  the  organized 
species  of  one  geological  epoch  were  transmuted  into 
those  of  another  by  some  long-continued  agency  of 
natural  causes  ; or  else  we  must  believe  in  many  suc- 
cessive acts  of  creation  and  extinction  of  species  out  of 
the  common  course  of  nature ; acts  which  therefore  we 
may  properly  call  marvellous.” — ( WhewelVs  Indica- 
tions of  the  Creator , p.  39.) 

Here  we  have  the  two  members  of  a Disjunctive 
stated  as  a Dilemma,  and  so  called  ; the  first  member 
is  considered  absurd  and  the  second  therefore  as 
true. 

722.  Another  form  of  the  Dilemma  is  sometimes 
Antecedents  used ; namely,  one  in  which  two  Antece- 

dictory <conse"  dents  are  affirmed  with  contradictory  Conse- 
quents, from  which  it  follows  of  course  that 


in.] 


OF  SYLLOGISMS. SECT.  XIV. 


181 


one  of  the  Antecedents  must  be  false.  Thus,  “ Lord 
Bacon  opposed  the  English  system  of  colonization  ; ” 
therefore,  “ If  Lord  Bacon  was  right,  the  English  sys- 
tem of  colonization  is  wrong.” 

But  if  the  English  are  right,  their  system  of  coloni- 
zation is  not  wrong ; therefore,  If  the  English  are  right, 
Lord  Bacon  was  not  right.  Or  if  Lord  Bacon  was 
right,  the  English  are  wrong. 


182 


LOGIC. PAKT  I. 


[CHAP. 


CHAPTER  IV. 

OF  FALLACIES. 


723.  We  have  already  noticed  the  difference  be- 
tween the  Form  and  the  Matter*  of  an  Argument,  and 

Errors  hcs  des  a^hough  the  Analysis  of  Formula  takes  no 
thoae’™in  Blthe  account  of  the  Matter,  and  supposes  that  the 
Formulas  are  valid  whatever  may  be  the 
Matter,  there  are  certain  sources  of  error  which  a mere 
inspection  of  the  Formulae  will  never  reveal  to  us. 
These  have  been  called  Fallacies.  It  is  not  easy  to 
collect  and  classify  them  all,  and  yet  something  of  the 
kind  is  indispensable. 

724.  A Fallacy  may  be  defined  in  its  broadest  and 

general  sense  to  be  any  fault  or  error  in  an  argument, 
Fallacies  de-  by  means  of  which  it  (1)  fails  to  prove  any 
fined-  thing  ; or  (2)  the  Conclusion  which  has  been 

assigned  to  it ; or  (3)  the  Conclusion  which  was  de- 
manded by  the  occasion  or  end  in  view. 

725.  It  has  been  customary  to  divide  Fallacies  into 
four  classes. — (1)  Fallacies  in  Form ; (2)  Fallacies  in 

Divided  into  Diction;  (3)  Fallacies  in  Matter;  and  (4) 
four  classes.  Extra-Logical  Fallacies.  The  differentia  of 
these  classes  is  not  very  distinctly  given  anywhere, 
nor  are  the  specific  names  used  with  any  great  uni- 
formity or  clearness.  We  may  perhaps  define  each 
species  as  follows : 


* See  Introduction,  14. 


IV.] 


OF  FALLACIES. 


183 


726.  Fallacies  are  in  Form  when  the  Formula  of- 
fends against  any  of  the  rules  of  the  mere  Fallacies  in 

Form,  and  is  perceptible  without  any  con-  Form- 
sideratiop.  of  the  Matter  of  the  Argument.  Hence 
Fallacies  imForm  should  rather  be  called  Faults  than 
Fallacies,  and  we  shall  so  designate  them  hereafter; 
and  then  a Fallacy  will  be  that  which  has  the  appear- 
ance of  a valid  Form,  and  deceives  by  its  appearance 
of  being  FaultZe&s.  It  does  not  fail  to  fulfil  called  Faults. 
the  formal  conditions  of  a proof,  but  fails  in  the  essen- 
tial conditions  which  lie  beneath  the  Form. 

727.  The  fallacy  may  he  said  to  be  in  Diction , 
when  the  words  in  which  it  is  stated  are  so  Fallacies  in 
used  as  to  leave  us  in  doubt  as  to  the  mean-  Diction- 
ing,  and  in  fact  so  as  to  have  several  meanings  in  the 
same  Formula. 

728.  The  Fallacy  may  be  considered  as  in  the 
Matter,  when  one  Premise  or  both  of  them  Fallacies  in 
are  taken  in  a sense  not  intended,  or  when  Matter- 
they  fail  to  express  the  judgment  adequately. 

729.  And  the  Fallacy  is  extra  Logical  when  it  lies 
beyond  the  Province  of  Logic  ; * as  when  it  Extra  Logicai 
states  as  a Premise  a Proposition  which  is  Faiiacie3- 
not  true ; or  proves  a Conclusion,  which  though  true 
enough,  is  not  to  the  purpose. 

730.  It  is  quite  possible  that  an  Argument  should 
offend  in  more  than  one  of  these  points  at  More  than  one 
the  same  time.  "We  must  however  remem-  JaajJaoy  ij^e 
her  that  a Fallacy  is  simply  a failure  to  ment- 
prove.  It  does  not  necessarily  follow  that  because  the 
Formula  contains  a Fallacy  therefore  the  Conclusion 
is  false  ; the  Conclusion  may  be  true  after  all,  and  all 
that  can  be  inferred  or  predicated  on  the  The  effect  of  a 
ground  of  the  Fallacy  is  simply  that  the  Con-  FaUacy- 
elusion  is  not  proved.  But  it  is  not  ^proved ; for 
disproof  implies  a concluding  force  in  the  Formula  of 
which  the  Fallacy  has  deprived  it. 


See  Introduction,  17. 


184 


LOGIC. — PART  I. 


[CHAP. 


Including  the  Extra  Logical  we  have  seven  distinct 
Enumeration  Fallacies,  excluding  Faults  in  Form  from 
of  Fallacies.  0ur  number  ; Ignoratio  Elenchi , Petitio 
Princvpii , and  the  five  in  the  use  of  the  Middle  Term.* 

• d 

* .Aristotle  [Soph.  Eleuch.],  and  after  him  most  other  writers,  reckons 
six  Fallacies  in  Dictione , and  seven  extra  Dictionem. 

The  six  in  Diction  are  : (1)  Equivocation,  as  “ the  dog  is  an  animal,  Si- 
rius [the  star]  is  a dog,  therefore  Sirins  is  an  animal ; ” (2)  Amphibolies,  as 
ap ’ '6  opq  t is,  t ovro  bpS,  or  as  Aldrich  gives  it,  Quod  tangitur  a Socrate  illud 
senXit ; Columna  tangitur  a Socrate : Ergo  Columna  sentit, — the  amphibology  is 
in  touto,  as  being  either  accusative  or  nominative,  and  in  the  Latin  exam- 
ple it  is  in  the  uncertainty  as  to  the  subject  of  sentit ; (3)  Composition ; and 
(4)  Division,  as  explained  below ; (5)  Accent,  as  when  putting  the  accent  on 
the  wrong  word,  or  the  wrong  syllable  in  a word,  we  give  it  a meaning 
different  from  that  which  was  intended  ; and  (0)  Figure  of  Speech,  where  on 
account  of  similarity  of  words  one  draws  a false  inference  from  one  to  the 
other,  as  because  Musa  is  of  the  feminine  gender  therefore  so  is  Poeta. 

The  seven  Fallacies  extra  Dictionem  are:  (1)  Fallacy  of  Accidents ; and 
(2)  a Dido  secundum  quid  ad  dictum  simpliciter,  as  explained  below ; (3)  Igno- 
ratio Elenchi ; (4)  A non  causa  pro  causa,  whether  it  be  a rum  vera  pro  vera, 
or  a non  tali  pro  tali.  As  an  example  of  the  first,  Aldrich  gives,  “ A comet 
shines — therefore  there  will  be  war.”  This  is  a non  causa,  the  comet  being 
entirely  innocent  of  causing  wars.  Of  the  second  he  gives,  “ Whatever 
will  intoxicate  is  forbidden  ; wine  intoxicates,  therefore  wine  is  forbidden.” 
“ Not  at  all,”  he  adds,  “ but  only  the  abuse  of  wine.”  Here  wine  is  ad- 
mitted to  be  a cause  of  intoxication,  but  it  is  prohibited  only  when  it  is 
such,  that  is,  in  sufficient  quantity  as  to  cause  intoxication  ; (5)  Fallacy  of 
Consequences,  as  when  a Conclusion  is  given  which  does  not  follow  from  the 
Premises — this  in  fact  includes  all  Fallacies  in  Form  ; (6)  Petitio  Principii, 
when  that  is  assumed  as  given  which  ought  to  have  been  proved  ; and 
(7)  the  Fallacy  of  Plurium  Interrogalionum,  when  several  questions  are  pro- 
posed as  if  they  were  one,  which  are  yet  so  related  to  each  other  as  to 
require  different  answers.  As,  “ .Are  honey  and  poison  sweet  ? Have  you 
left  off  your  bad  habits  ? ” 

These  thirteen  Fallacies  have  been  arranged  into  mnemonic  lines ; 
thus, 

-ZEQUTVOCAT.  AMPHI.  COMPONIT,  DIVIDIT,  ACC.  FI. 

ACCI.  QUID.  IGNORANS,  NON  CAUSA,  CON.  PETIT.  INTERR. 

But  I have  preferred  the  classification  given  above  in  the  text,  for  rea- 
sons I will  not  enumerate  here  ; the  1st,  2d,  and  6th  are  included  under 
Ambiguous  Middle  ; the  5th,  Accent,  does  not  belong  to  Logic  at  all — at 
least  it  is  a mere  trick  ; the  same  may  be  said  of  the  13th,  Plurium  Interro- 
gationum ; the  11th  I have  reckoned  under  the  head  of  Faults  in  Form; 
the  3d  and  4th  I have  recognized  by  name,  as  also  the  7th,  8th,  and  9th  ; 
the  10th,  Non  Causa , I have  included  under  the  more  general  head  of  the 
Petitio  Principii. 


OF  FALLACIES. — SECT.  I. 


185 


rv.] 


SECTION  I. 

Of  the  Ignoratio  Elenchi , or  Mistaking  the  Issue. 

A % A 

The  words  Ignoratio  Elenchi  mean  “ Ignorance  of 
the  Proof”  which  ought  to  be  given,  and  ignoratio Eien- 
are  applied  equally  to  cases  in  which  one  is  i^Lratherthin 
really  and  innocently  ignorant,  and  to  those  aFallacy- 
in  which  one  chooses  to  ignore  the  real  issue  to  be  met 
and  the  Proof  necessary  to  meet  it.  In  this  view  of  it, 
therefore,  it  is  not  a Fallacy  in  Logic  at  all,  but  simply 
a fault  in  sagacity  or  honesty,  or  both.  It  is  no  fault 
in  Form  nor  a fallacy  in  the  use  of  Forms.  It  is  no 
fault  in  Method,  for  the  Formula  and  Method  may 
both  be  faultless.  It  is  therefore  merely  a failure  to 
pursue  the  right  End — a failure  in  Aim  or  End  ; as 
disastrous  of  course  to  the  success  of  an  Argument  as 
any  fallacy  can  be,  but  differing  in  kind  both  from 
Fallacies  in  the  uses  of  Formula  and  Faults  in  Me- 
thod. 

731.  Nothing  can  he  more  important  in  the  con- 
struction of  an  argument  than  a clear  and  [mp„tar,ceof 
adequate  conception  of  the  precise  point  to  therightEnd- 
he  proved.  Without  this  we  may  deceive  ourselves 
or  be  imposed  upon  by  others. 

732.  The  Ignoratio  Elenchi , or  mistake  of  the  Ques- 
tion, is  more  pernicious  when  it  occurs  in  a where  ignora- 

p x i . . tio  is  likely  to 

course  ot  reasoning  where  an  argument  is  occur, 
introduced  merely  as  subservient  to  some  more  general 
purpose  or  conclusion  than  elsewhere.  In  this  case  the 
deception  is  less  likely  to  be  detected,  and  the  tempta- 
tion to  it  is  much  stronger  than  any  where  else. 

733.  We  have  an  illustration  of  this  fallacy  pointed 
out  in  the  speech  of  Diodatus,  given  in-  Thucydides,  in 
answer  to  Cleon,  who  had  argued  that  it  illustration  from 
would  be  just  to  put  the  Mitylenians  to  ThucJ’dldes- 
death.  Diodatus  reminds  him  that  that  was  not  the 
question ; the  question  really  before  them  was  whe- 


186 


LOGIC. — PAJBT  I. 


[chap. 


tlier  it  would  be  expedient  for  the  Athenians  in  their 
present  circumstances  to  undertake  it.* 

734.  Mistakes  of  this  kind  will  be  found  on  a careful 
thf/'kmd3 fref  scrutin.y  of  far  more  frequent  occurrence 
quent.  r than  one  would  at  first  exppcl^?  and  nothing 
but  the  most  careful  scrutiny  and  the  most  sagacious 
discrimination  of  things  similar  in  appearance,  but  dif- 
ferent in  reality,  can  secure  immunity  from  this  kind 
of  imposture. 


SECTION  II. 

Of  the  Petitio  Principii. 

Under  this  head  I shall  include  all  forms  of  assum- 
ing for  Premises  what  ought  not  to  be  assumed,  or  used 
as  such  without  being  first  proved  to  be  true  in  the 
sense  and  to  the  extent  used. 

735.  Strictly  speaking,  the  Petitio  Principii  is  the 
petiuoPrinci - fault  in  Method  which  consists  in  stating  as 
Sin  Method  a Premise  a Proposition  which  contains  the 
Conclusion,  in  such  a way  as  that  it  can  be  evolved 
from  the  Premise  by  some  of  the  processes  of  Imme- 
diate Inference. 

736.  In  the  popular  sense  it  means  simply  the 
The  popular  assuming  as  true  that  which  we  are  expect- 

word.  mg  or  wishing  to  have  proved.  It  is  seldom 

the  case  that  both  Premises  of  an  Argument  are  dis- 
puted or  questioned,!  and  ivhen  the  one  that  is  thus 

* Thucydides,  Book  III,  Year  5. 

f For  this  reason  some  writers,  and  writers  on  “Logic,”  even,  have 
maintained  that  every  Syllogism  is  a Petitio  Principii.  They  cite  such  exam- 
ples as  the  following : 

All  men  are  mortal ; 

John  Smith  is  a man  : 

.-.  John  Smith  is  mortal. 

But,  say  they,  the  Major  cannot  be  affirmed  as  true  unless  John  Smith 
be  mortal.  They  forget  that  they  beg  the  question  themselves — the  ques- 
tion, to  wit,  whether  John  Smith  is  a man  or  not. 

Let  us  take  a case  in  which  both  Premises  admit  of  doubt,  or  are  at 
least  denied  : 


IV.] 


OF  FALLACIES. — SECT.  II. 


187 


questioned  is  assumed,  the  assumption  is  regarded  as  a 
begging  of  the  principle  or  main  Premise  on  which 
the  Conclusion  depends. 

737.  We  have  several  forms  of  Premises  unduly 
assumed,  or  untrue.  We  must,  however,  distinguish 
between  a fallacy  and  a falsehood,  or  mere  of  pre 
false  statement.  It  is  no  part  of  Logic  to  mises  not  a Fal- 
ascertain  whether  Propositions  introduced  aoy' 
as  Premises  are  true  or  false ; thus,  If  a man  affirms 
that  A is  B,  when  it  is  not  so,  the  false  statement  is 
not  a Fallacy  for  Logic  to  correct;  but  it  is  a misstate- 
ment to  be  corrected  by  investigation  into  the  subject 
matter  of  the  Proposition.*  The  truth  is  to  be  sought  in 

No  murderer  hath  eternal  life  ; 

All  warriors  are  murderers : 

Therefore  No  warrior  hath  eternal  life. 

Here  we  have  a Major  Premise  which  some  professing  Christians  deny, 
and  others  would  of  course  deny  the  Minor.  Hence  in  the  estimation  of  some 
persons  one  Premise  might  be  affirmed  without  involving  the  truth  of  the 
Conclusion,  and  in  the  estimation  of  another  class  the  other  Premise  might 
be  affirmed  without  involving  its  truth.  In  this  case,  therefore,  neither  Pre- 
mise can  be  regarded  as  a Petitio  Principii.  But  this  differs  from  others 
so  far  as  this  point  is  concerned,  only  in  the  purely  accidental  fact,  that 
either  one  of  its  Premises  are  such  as  to  he  denied  or  doubted  by  any  body. 

* It  certainly  diminishes  our  reverence  for  Akistotle  immensely,  to 
find  that  in  his  Prior  Analytics,  Book  II,  he  has  devoted  three  chapters,  II, 
HI,  and  IV,  to  the  consideration  of  the  cases  and  conditions  in  which  we 
may  have  a true  Conclusion  from  False  Premises  ! If  one  could,  he  would 
disbelieve  that  these  chapters  ever  came  from  the  Stagyrite.  But  there  is 
no  help  for  it  that  I can  see  ; I find  no  intimation  of  their  spuriousness. 

That  there  may  be  no  mistake  about  the  matter,  and  that  the  reader 
may  see  what  cases  the  Father  of  Logic  is  discussing,  I will  give  an  exam- 
ple : “ As  animal  is  with  no  stone,  nor  stone  present  with  any  man,  yet  if 
animal  is  predicated  of  stone,  and  stone  of  man,  we  shall  yet  have  the  Con- 
clusion, man  is  an  animal.”  Thus, 

“ Every  stone  is  an  animal ; 

Every  man  is  a stone  : 

.".  Every  man  is  an  animal.” 

The  Conclusion  is  undoubtedly  true  ; and  it  i sfrom,  and  a good  'wa.ys.from, 
the  Premises  too.  We  might  just  all  well  substitute  “ jack-knife  ” for  Minor 
term,  and  prove  by  the  same  formula  that  a “jack-knife”  is  a man. 

It  is  no  wonder  that  Logic  has  fallen  into  disrepute  when  we  find  the 
Father  of  the  Science  indulging  in  such  ridiculous  nonsense.  Had  this 
acutest  of  men  got  bewildered  with  the  intricacy  of  his  own  system,  aban- 


188 


LOGIC. — PAKT  I. 


[chap. 


History,  in  Science,  in  Observation,  &c.  &c.  The  whole 
realm  of  knowledge  is  to  be  put  in  requisition  to  deter- 
mine the  truth  or  falsehood  of  Propositions  when  used 
as  Premises.  Logic  is  responsible  only  for  the  truth  of 
the  Conclusion  on  condition  that  the  Premises  are  true. 

The  assumptions  under  this  head  are  reckoned  by 
sumption?  Aa  the  °ld  writers  as  two  : 

738.  (1.)  A non  vera  causa  pro  verd  causd.  As 
when  we  say,  “ There  is  a comet,  therefore  there  will 
be  a pestilence.”  The  completion  of  this  Enthymeme 

Non vem pro  would  imply  the  assertion,  that  “comets 
vera-  cause  pestilence,”  or  “ whenever  there  is  a 

comet  there  is  a pestilence ; ” the  latter  of  which 
statements  is  simply  untrue,  the  former  assigning  for  a 
cause  that  which  is  not  a cause  of  the  effect.  Hence 
a non  vera  pro  vera , as  it  is  usually  written  (omitting 
the  word  causa),  is  stating  as  a Premise  that  which  is 
untrue. 

739.  (2.)  A non  tali  [causd)  pro  tali  [causa.)  As, 
“ Whatever  is  poisonous  should  never  be  taken.  But 

Non  tan  pro  opium  is  poisonous.”  In  this  case  it  is  ad- 
tali-  mitted  that  opium  is  poisonous — that  it  is  a 

cause  of  death,  but  a cause  of  death  only  when  taken 
in  certain  quantities  or  in  certain  ways. 

To  these  we  may  add  one  or  two  others  : 

740.  (1)  When  in  categorical  Premises  the  two 
relate  to  different  points  of  time,  as,  “ He  who  is  most 

hungry  eats  most.  But  he  that  eats  most  is 
of0tFaiseFoTas  least  hungry,  therefore  he  that  is  most  hun- 
gry is  least  hungry.”  These  Premises  refer 
to  different  points  of  time  in  relation  to  the  act  of 
eating ; (2)  then  we  may  have  want  of  sequence  in 
Conditionals  ; (3)  non-exclusion  of  Middle  in  Disjunc- 
tives ; (4)  want  of  sameness  in  kind  in  things  compared 
in  Comparatives. 

doned  his  a priori  light,  and  set  himself  to  justify  by  hook  or  by  crook,  as 
best  he  could,  every  possible  Formula  to  which  a Conclusion  which  is  true  as 
an  independent  Proposition,  though  not  as  a Conclusion,  might  be  attached  ? 
It  would  seem  so. 


JV.] 


OF  FALLACIES. — SECT.  ILL 


189 


SECTION  m. 

Of  Ambiguous  Middle. 

741.  Hot  only  must  the  Middle  Term  be  once  taken 
as  a Whole,  but  it  must  be  used  in  both  Pre-  Ambiguous 
mises  in  the  same  sense ; otherwise  we  have  Middle- 
the  Fallacy  in  Diction  of  Ambiguous  Middle. 

742.  A word  may  be  equivocal  in  itself,  or  intrin- 
sically, as  in  fact  many  words  are,  so  that  -words  intrinsic- 
we  really  do  not  know  precisely  wliat  one  ally  amb'"uous- 
intends  by  bis  Proposition,  until  we  have  beard  him 
discourse  long  enough  to  render  bis  terms  perspicuous. 
Thus  if  one  were  speaking  of  “ beat  ” in  a scientific 
treatise,  we  should  be  in  doubt  whether  by  the  word 
be  meant  that  specific  beat  which  is  perceptible  to  the 
senses,  or  that  latent  heat  which  exists  in  all  bodies  to 
a greater  or  less  extent  and  yet  produces  no  effects 
upon  the  thermometer.  And  yet  a Proposition  might 
be  true  or  false  as  the  term  was  used  in  one  or  another 
of  these  senses. 

743.  But  if  the  Middle  Term  is  taken  in  a different 
sense  in  each  Premise,  it  is  the  same  so  far  The  Middle 
as  all  purposes  of  deduction  are  concerned,  S|uou“ylathe 
as  if  these  were  two  entirely  unlike  and  dif-  Sjle  $?enj£“ 
ferent  terms. 

744.  “It is  worthobserving,”  says  Whately,*  “that 
the  words  whose  ambiguity  is  the  most  fre-  Word3  whose 
quently  overlooked,  and  is  productive  of  the  m“stTreqyuentiy 
greatest  amount  of  confusion  of  thought  and  ovcrlooked- 
fallacy  are  among  the  commonest , and  are  those  of 
whose  meaning  the  generality  consider  there  is  the 
least  room  to  doubt.  It  is  indeed  from  these  very  cir- 
cumstances that  the  danger  arises ; words  in  very 
common  use  are  both  the  most  liable  from  the  loose- 
ness of  ordinary  discourse,  to  slide  from  one  sense  into 


Appendix,  No.  I. 


190  LOGIC. — PART  I.  [CHAP. 

another,  and  also  the  least  likely  to  have  that  ambi- 
guity suspected.” 

745.  The  Archbishop  has  collected  some  forty  or 
Habitual  cau-  fifty  words  illustrative  of  the  foregoing  re- 
Bafesuard.  °" 5 maim  But  its  truth  and  force  can  be  appre- 
ciated only  after  a long-continued  habit  of  carefully 
noticing  the  meaning  of  words  as  they  are  used  in 
ordinary  conversation  and  in  the  printed  works,  espe- 
cially those  of  a controversial  character.  A large  part 
of  all  the  controversy  that  has  ever  existed  in  the  world 
has  risen  from  persons  calling  the  same  thing  by  dif- 
ferent names,  or  by  their  meaning  very  different  things 
when  they  use  the  same  name  or  term. 

746.  The  Fallacy  of  Ambiguous  Middle  is  spoken 
several  varie-  of  in  several  different  ways,  but  it  is  in  all 
ties  o ambit, ur  (Fese  classes  (if  we  are  to  regard  these  dif- 
ferent names  as  indicating  different  classes)  essentially 
the  same.  Thus  we  have  the  Fallacy  of  Equivocation 
when  the  same  word  is  used  in  different  senses.  The 
Fallacy  of  Amphibology  when  the  word  is  used  so  as  to 
admit  of  different  senses  in  each  Premise.  The  Fallacy 
of  Figure  of  Speech  when  the  Middle  Term  is  used 
metaphorically  in  one  Premise ; and  the  Fallacy  of 
Paronomasia  &c. 


SECTION  IV. 

Of  the  Fallacy  of  Division  and  Composition. 

747.  This  Fallacy  consists  in  using  the  Middle  Term 
in  one  Premise  as  a General  Term,  and  in  the  other  as 
a Collective  Term. 

If  now  we  use  the  Middle  Term  as  a Collective 
Fallacy  of  Divi-  Term  in  the  Major,  and  as  a General  Term 
Bion-  in  the  Minor  Premise,  we  have  the  Fallacy 

of  Division  ; thus, 

The  Romans  [collectively]  destroyed  Carthage  ; 

Brutus  was  a Roman  [that  is,  belonged  to  the  Ge- 
nus Roman]  : 

.-.Brutus  destroyed  Carthage. 


IV.] 


OF  FALLACIES. SECT.  V. 


191 


748.  But  if  the  Middle  Term  is  used  generally,  or  as 
a General  Term  in  the  Major  Premise,  and  FaiiaCyofcom- 
collectively,  or  as  a Collective  Term  in  the  position- 
Minor,  we  have  what  is  called  the  Fallacy  of  Compo- 
sition ’ thus, 

Three  and  two  are  two  numbers  ; 

Five  is  two  and  three  [collectively]  : 

.\  Five  is  two  numbers. 


749.  “ This  is  a Fallacy  with  which  men  are  ex- 
ceedingly apt  to  deceive  themselves,”  says  Wliately ; 
“ for  when  a multitude  of  particulars  are  presented  to 
the  mind,  many  are  too  weak  or  too  indolent  to  take  a 
comprehensive  view,  but  confine  their  atten- 


The  spend 


tion  to  each  single  point  by  turns  and  thus  thrirt’s  Fallacy- 
decide,  infer,  and  act  accordingly.  For  example,  the 
imprudent  spendthrift  finding  that  he  cannot  afford  a 
certain  great  expenditure  as  a whole,  resolves  upon 
each  of  its  parts  separately,  forgetting  that  all  of  them 
together  will  ruin  him.” 


SECTION  V. 

Fallacy  of  Accidents  and  of  Quid. 

750.  The  first,  Fallacia  Accidentis , occurs  when- 
ever in  the  course  of  the  syllogism  a term  Fa,lacy  of 
has  been  predicated  of  another,  in  reference  Accidents- 
to  its  essential  and  inseparable  properties,  and  taken 
as  predicated  of  its  separable  accidents  A 
What  we  buy  in  the  market  we  eat ; 

W e buy  raw  meat  in  the  market : 

.•.  Raw  meat  is  what  we  eat ; or,  “ we  eat  raw  meat.” 
Here  the  Middle  Term  is  predicated  of  the  Minor 
essentially,  and  thus  by  means  of  the  Middle  Term  the 
Major  is  predicated  of  the  Minor,  as  if  the  Middle  had 
been  predicated  of  the  Accidents  rather  than  the  Es- 
sentia of  the  Minor. 


* See  Chap.  II.,  220. 


192 


LOGIC. — PAKT  I. 


[chap. 


751.  The  Fallacy,  a dicto  secundum  quid  ad  dictum 
simpliciter,  called  for  the  sake  of  brevity  the  Fallacy 

Fallacy  of  °1'  Quid,  is  that  in  which  the  Middle  Term 
Quid-  is  taken  in  one  Premise  as  used  in  its  broad- 

est signification,  and  in  the  other  as  used  only  with 
reference  to  some  special  subject  or  application. 

As  for  example,  when  it  is  inferred  from  the  decla- 
rations concerning  the  Virgin  Mary,  that  she  was  pure 
and  immaculate  [as  a virgin],  that  therefore  she  was 
sinless  [as  an  accountable  being],  and  so  must  have 
been  born  without  any  taint  of  human  depravity. 

But  the  pureness  and  immaculateness  as  to  virginity 
is  one  thing  and  absolute  purity  is  quite  another,  and 
cannot  be  inferred  from  it.  The  fallacy  is  precisely 
the  same  as  that  made  by  the  passenger  in  a railroad 
car  when  on  seeing  the  notice,  “ No  smoking  allowed 
here,”  he  inferred  that  the  stove  would  not  smoke. 

As  another  illustration  take  the  following  : 

Nebuchadnezzar  ate  grass  like  the  oxen  ; 

But  the  oxen  eat  grass  standing  on  hoofs  and 
chewing  the  cud : 

.•.  Nebuchadnezzar  had  hoofs  and  chewed  the  cud. 

752.  This  Fallacy  it  will  be  seen  arises  from  a dis- 
Mo?t  assertions  regard  of  the  scope  and  design  of  a writer, 
scope d in  tlie‘r  In  fact  it  is  but  seldom  that  any  proposition  is 
affirmed  except  when  there  is  some  special  end  in  view, 
or  some  special  object  before  the  mind  in  reference  to 
which  it  is  true  ; while  in  an  application  to  objects  of 
another  class  it  might  be  entirely  false. 

753.  Besides  the  foregoing  Fallacies,  Whately  has 
enumerated  several  others  which  are  merely  Tricks  of 
the  Rhetorician’s  Art,  and  the  consideration  of  which 
does  not  belong  to  a Treatise  on  Logic. 

We  have  defined  Faults  as  failures  to  fulfil  the 
Formal  conditions  of  an  Argument,  and  Fallacies 

Tricks  as  dif-  as  failures  to  fulfil  the  Essential  conditions 
FaX  or  me”  lying  beneath  the  mere  form.  But  a Trick 
Fallacies.  js  something  which  fails  to  be  a Fault  even. 


IV.] 


OF  FALLACIES. SECT.  V. 


193 


A Fault  can  always  be  reduced  to  some  Formula,  one 
of  the  sixty-four  Moods,  though  an  invalid  one.  But 
a mere  Trick  has  not  the  elements  to  complete  any 
Formula.  It  cannot  be  put  into  the  form  or  shape  of 
an  Argument,  however  successful  it  may  sometimes 
prove  in  carrying  a point  and  producing  the  legitimate 
results  of  sound  reasoning. 


PART  II. 

OF  LOGICAL  METHODS. 


CHAPTER  I. 

OF  THE  ELEMENTS  OF  METHOD. 


SECTION  I. 

Of  Method  in  General. 

754.  Method  is  the  way  in  which  the  means  to  any 
Method  defined,  end  ave  used  for  its  accomplishment.  Con- 
sequently Method  always  supposes  an  End  or  object 
in  view,  Matter  in  which  it  is  to  he  accomplished, 

supposes  an  Means  to  be  used  in  its  accomplishment. 

End,  Matter,  A . . , n t 1 . 7 

and  Means.  and  an  Agent  to  use  them  ; — the  word  is 
from  the  Greek  fied'  ohov.  Thus  if  I wish  to  be  in  a 
neighboring  village,  the  road  by  which  I go  thither  is 
my  Method,  while  the  carriage  in  which  I ride,  or 
my  feet  if  I walk,  are  the  Means  which  I use  by  the 
way. 

755.  Method  itself,  however,  may  he  resolved  into 
several  elements;  as,  (1)  Method,. properly  so  called, 

Elements  of  that  is,  the  way  by  which  one  shall  go,  as 
Method.  jn  going  from  one  place  to  another  ; (2)  the 
Order  in  which  the  several  steps  shall  be  taken,  as 
which  first,  and  which  next,  and  so  on  ; and  (3)  the 
Manner  in  which  each  step  shall  be  taken.  In  going 


CHAP.  I.]  OF  THE  ELEMENTS  OE  METHOD. SECT.  I.  195 


to  a neighboring  village  there  is  no  room  for  choice, 
as  to  which  step  shall  be  taken  first  in  order,  hut  one 
might  take  it  into  his  head  to  walk  sideways  or  back- 
wards. In  this  case  his  Method  and  Order  might  be 
perfectly  good,  hut  his  Manner  would  be  very  awk- 
ward. In  a general  sense,  however,  all  three  of  these 
elements  are  included  in  Method  ; and  Order  and  Man- 
ner themselves  become  but  the  Method  of  the  subordi- 
nate parts  of  any  whole  with  reference  to  which  the 
word  Method  is  used. 

756.  Method  gives  unity  of  plan  and  efficiency  in 
the  use  of  means  towards  the  attainment  of  Method  gives 

-i  t,  • i -i  * . -1  i , unity  and  effi- 

any  end.  It  is  not  always  the  strongest  man  ciency. 
that  can  accomplish  the  most  work  in  a given  time, 
nor  the  fleetest  of  foot  that  can  make  the  quickest  race. 
Inferior  force  is  often  rendered  the  most  efficient  by 
the  superiority  of  Method.  Method  has  to  do  with 
every  thing.  Method  is  the  result  of  mental  power 
and  application.  It  indicates  capacity  and  attention, 
as  its  absence  indicates  the  want  of  them. 

757.  Hence  Method  must  form  an  essential  part 
of  any  trade  or  art  that  is  to  be  learned.  It  Method  is  the 
is  in  fact  the  conversion  of  Science  into  Art,  Knowledge  “o 
the  passing  from  knowledge  to  practice.  practice. 

758.  The  beauty  of  any  operation  depends  upon 
the  Order  and  Method  pursued  in  it,  and  the  Beauty  of  ope- 

t .1  . • j i i i ration  depends 

pleasure  or  the  pam  with  which  any  accom-  upon  Method, 
plislied  performer  in  any  department  of  human  activity 
watches  the  acts  of  another  depends  upon  the  presence 
or  absence  of  Method  in  the  operator.  And  a quick 
insight  into  the  Method  of  any  act  or  series  of  actions 
is  called  genius  for  that  kind  of  actions. 

759.  In  writing  or  speaking,  not  only  the  order  in 
which  the  sentences  follow  one  another,  but  Force  of  writ- 
also  that  in  which  the  words  are  placed  merits  depend 

1 , • i , i h upon  their  Me- 

relatively  to  each  other  in  each  sentence,  thod. 
depends  upon  Method  ; and  upon  this  arrangement 
depends  the  beauty  and  force  of  what  is  said  or  writ- 
ten. In  a mathematical  demonstration  there  is  a cer- 


196 


LOGIC. PAKT  II. 


[ci-IAP. 


tain  method  or  order  in  which  the  steps  should  he 
taken — and  we  should  hardly  call  that  a demonstra- 
tion, which  although  it  had  included  all  that  was 
necessary,  had  thrown  the  parts  together  in  entire 
disregard  of  the  order  in  which  they  ought  to  follow 
each  other.  Such  a demonstration,  if  demonstration  it 
could  be  called,  would  demonstrate  the  want  of  capa- 
city in  the  demonstrator  rather  than  the  truth  of  the 
Proposition  to  be  proved. 

SECTION  II. 

Of  Order  as  an  Element  of  Method. 

760.  Method  always  implies  an  End,  and  yet  it  is 
not  concerned  in  the  selection  of  that  End.  It  is  con- 

Ends  deter-  cerned  merely  with  its  attainment.  The 
”ins|ty  laid  Ni>y  Eiid  may  be  determined  for  us,  or  we  may 
choice.  be  igp-  f-0  c]100se  it  for  ourselves.  Ethics 
determine  Ends  for  us  when  it  specifies  certain  acts  as 
being  of  moral  obligation,  and  which  therefore  we  are 
not  at  liberty  to  do  otherwise  than  pursue.  Theology 
determines  Ends  for  us  by  showing  acts  which  by 
the  Will  and  Command  of  God  are  obligatory  upon 
us.  Polity  determines  Ends  for  us,  as  when  the  State 
commands  certain  acts  by  its  positive  enactments. 
Necessity  determines  Ends  for  us  when  by  a fixed  law 
of  our  nature  it  is  ordained  that  we  must  eat  to  live, 
and  must  work  in  order  to  have  something  to  eat. 
But  in  regard  to  many  of  our  acts  we  are  left  to  select 
our  Ends  for  ourselves,  as  Pleasure,  or  Interest,  or 
Benevolence  may  incline  us. 

761.  Order,  however,  is  an  important  element  in 
order  neces-  Method,  and  there  can  be  no  Method  with- 
thod.  lo  ML"  out  Order.  The  Principles  of  Order  how- 
ever are  very  few  and  simple,  and  the  same  in  all 
departments  of  human  activity.  Always  there  is  a 
place  to  begin,  a place  to  end,  and  intermediate  steps 
to  be  arranged.  That  step  or  act  which  presupposes 


X.]  OF  THE  ELEMENTS  OF  METHOD. SECT.  II.  197 

others  cannot  well  be  taken  first,  and  that  which  is 
necessary  to  the  succeeding  cannot  well  he  order  to  some 
postponed  to  the  last.  The  mason  cannot  byp- 
lay the  wall  until  the  stone,  and  lime,  and  cessity- 
sand  have  been  drawn  and  the  mortar  made.  The 
carpenter  cannot  dress  the  timber  and  fit  each  piece 
to  its  place,  until  the  trees  have  been  felled  and  the 
hoards  hauled  to  the  place  where  they  are  to  be  used. 
So  in  studies  — the  alphabet  must  be  learned  first, 
geometry  must  be  learned  before  trigonometry,  and 
grammar  before  rhetoric ; and  he  that  should  under- 
take the  calculus  before  algebra,  or  history  before  he 
knew  any  thing  of  geography,  would  find  that  he  had 
made  a mistake  in  Method,  which  would  render  all  his 
studies  and  his  efforts  unavailing. 

762.  That  fault  in  Method  which  consists  in  invert- 
ing the  true  order  of  the  steps,  or  successive  The  FauIt  of 
acts  in  any  series  of  actions,  has  been  called  later^rs!- 
by  the  Greek  writers  a varepov  irpoorov,  that  is,  a later- 
jvrst. 

763.  In  every  process  there  are  some  of  the  steps 
or  elements  whose  position  is  fixed  by  the  very  nature 
and  necessities  of  the  case.  Thus  in  the 

, . n i , • i The  Order  of 

erection  oi  a house  the  materials  must  be  many  steps  left 
hauled  to  the  spot  before  the  walls  can  he  t0ch0ice- 
put  up.  But  in  every  process  also  there  is  a large 
number  of  elements  or  steps,  the  position  of  which  is 
not  so  determined  by  the  nature  and  necessities  of  the 
case  as  that  there  may  not  be  varieties  in  the  order ; 
and  their  disposal  furnishes  a sphere  for  the  exercise 
of  tact  and  genius. 

7 61.  The  five  great  Canons  of  Order  are  : ofF6'rderCanons 

(1.)  Place  that’ first  which  presupposes  nothing  as 
having  preceded  it. 

(2.)  Put  that  last  which  presupposes  all  the  rest, 
and  neither  conduces  to  nor  implies  any  thing  to  fol- 
low it. 

(3.)  Put  each  intermediate  step  after  that  which  it 
presupposes,  and  before  all  those  which  depend  upon  it. 


198  LOGIC. — PART  II.  [CHAP. 

(4.)  Omit  as  extraneous  matter  whatever  is  not 
conducive  to  the  End  in  view. 

(5.)  If  there  are  intermediate  steps  requiring  to 
occupy  the  same  place,  they  may  he  arranged  with 
regard  to  convenience  or  taste  merely. 

765.  Method  can  never  be  discussed  and  treated  in 
any  full  and  satisfactory  way,  except  in  connection 
The  discussion  with  a discussion  of  the  Means  and  the  Mat- 

ter,  or  at  least  by  presuming  that  they  are 
Matter  and  the  already  known.  To  teach  the  Method  of 
Means.  any  trade  or  art  would  he  to  teach  the  trade 
or  art  itself.  We  could  not  teach  the  Method  of  ship- 
building, for  instance,  without  teaching  the  whole  trade 
of  building  ships.  For  the  order  in  which  each  act 
should  come,  each  material  he  used,  and  the  way  in 
which  these  details  should  be  disposed  of,  must  depend 
upon  the  character  of  the  details  themselves  to  such  an 
extent  as  to  involve  Method  and  Means  most  inextri- 
cably in  the  same  discussion. 

766.  For  this  reason  it  will  he  necessary  to  limit 
Means  of  limit-  ourselves  in  the  discussion  to  some  special 
ject. the  feulJ-  and  definite  sphere.  This  we  shall  best  ac- 
complish by  considering  those  influences  which  are 
external  to  Method  itself  properly  considered,  but, 
which  do  nevertheless  determine  it,  and  constitute 
species  and  varieties  in  Method. 

SECTION  III. 

Of  the  Ideas  which  determine  Method. 

767.  I have  said  that  Method  is  the  result  of  mind 
in  its  application  to  the  attainment  of  any  End. 

768.  But  there  may  be  several  W ays  or  Methods  to 
several  Me-  the  same  End.  If  1 wish  to  go  to  the  neigh- 
same3  E^d.  the  boring  village,  for  instance,  I may  wish  to 
go  as  quickly  as  possible  ; in  that  case  I should  select 
my  means  and  my  method  or  way  with  reference  to 
quickness  of  time.  If  the  time  is  no  object,  the  ease 


I.]  OF  THE  ELEMENTS  OF  METHOD. SECT.  III.  199 


with  which  the  journey  may  be  accomplished  may 
determine  me  to  select  other  means  and  another  route. 
Or  again,  if  pleasure  be  the  leading  object,  I may  select 
still  different  means  and  still  a different  route  from 
what  I should  if  speed  or  ease  alone  were  to  be  con- 
sulted. 

769.  There  are  Five  Ideas  which  determine  the 
mind  in  its  choice  of  a Method — two  of  them  Five  ideas  that 
are  relative — Ideas  of  the  Understanding,  as  thodsmine  We' 
the  Germans  would  call  them ; and  three  are  abso- 
lute— Ideas  of  the  Reason.  The  two  former  are  Plea- 
sure and  UriLrrY ; the  three  latter  are  the  Good,  the 
Beautiful,  and  the  True.* 

770.  The  two  former,  Pleasure  and  Utility,  I have 
called  relative  Ideas,  because  they  always  pleasure,  why 
relate  to  the  person  by  whom  the  Method  is  relative- 
determined.  What  is  pleasant  is  pleasant  not  abso- 
lutely and  in  itself,  hut  only  because  it  is  found  to 
afford  pleasure  to  him  who  experiences  it ; the  same 
thing,  as  we  often  see,  may  be  pleasant  to  one  and  un- 
pleasant to  another. 

771.  So  of  Utility.  Nothing  is  useful  in  itself  or 
absolutely.  It  is  useful  only  to  some  end;  utility ahore- 
and  the  end  by  comparison  with  which  we  Iative- 
judge  a thing  to  be  useful  is  also  personal  and  of  time. 
If  we  ask  why  a thing  is  useful,  wTe  always  come  round 
at  last  as  the  final  answer  to  the  fact,  that  it  conduces 
to  some  worldly  object  which  we  wush  to  have  accom- 
plished. 

772.  But  the  Good,  the  Beautiful,  and  the  True  are 
absolute.  To  say  that  a thing  is  Beautiful  The  Good  the 
because  it  pleases,  is  merely  to  give  our  fhee  True,’  a'bTod 
means  of  knowing  a thing  for  the  reality  of  Iute- 

* There  may  be  good  reasons  for  reckoning  tbe  Plausible  as  sustaining 
the  same  relation  to  the  True  that  the  Pleasant  does  to  the  Beautiful,  and 
the  Useful  to  the  Good.  But  I have  chosen  not  to  do  so  ; hut  rather  to 
look  upon  the  Plausible  as  merely  one  subordinate  species  of  the  Useful ; 
namely,  that  which  is  useful  for  conviction  and  persuasion,  irrespective  of 
the  truth  of  that  which  those  whom  we  address  are  to  be  persuaded  or 
oonvinced  to  do. 


200 


LOGIC. — PART  II. 


[chap. 


the  tiling  itself.  To  say  that  an  act  is  good  because  it 
is  useful  is  to  change  the  standard  altogether.  The 
absurdity  of  the  change  is  seen,  when  instead  of  speak- 
ing of  moral  excellence  or  the  character  of  God,  we 
say  that  it  is  Useful  instead  of  it  is  Good. 

773.  The  life  of  man  is  for  the  most  part  controlled 
and  directed  by  the  relative  Ideas  of  Utility  and  Plea- 

The  r eiative  sure-  Devotion  to  the  absolute  Ideas  im- 
ideasemostailr'oe  plies  something  of  self-forgetfulness  and 
ordinary  nie  of  self-immolation  that  rises  into  heroism  and 
religion.  It  implies  an  elevation  and  dignity 
of  character  which  is  by  no  means  every  where  to  be 
met  with. 

774.  These  several  Ideas  when  developed  into  prac- 
These  ideas  tical  precepts,  give  rise  to  systems  or  codes1 

rules  of  action.0  of  action.  Thus  the  Idea  of  Pleasure  be- 
comes the  Epicurean  theory  of  Ethics.  Pleasure  is  the 
Highest  Good,  and  Virtue  is  only  the  wise  and  pru- 
dent pursuit  of  Pleasure.  The  Idea  of  Utility  gives 
rise  to  the  system  of  expediency,  the  Happiness  of 
Man  ; and  each  one’s  happiness  is  for  himself  the  High- 
est Good  -which  he  can  propose  to  himself  to  accom- 
plish. Hence  whatever  is  useful  towards  the  accom- 
plishment of  this  end  is  right,  and  the  pursuit  of  it  is 
virtue. 

775.  The  Idea  of  the  Beautiful  is  developed  into 
Development  what  lias  come  to  be  called  ^Esthetics  ; and 

ideas.  A sullUe  the  Idea  of  the  Good  determines  Ethics,  or 
the  law  of  right  action.  And  Logic  in  its  comprehen- 
sive sense  is  determined  by  the  Idea  of  Truth.  Aes- 
thetics says  this  must  be  so  because  it  is  beautiful. 
Ethics  says  this  must  be  so  because  it  is  right , and 
Logic  says  this  must  be  so  because  so  it  is  conformed 
to  Truth. 

776.  These  Ideas  sustain  towards  each  other  a sort 
Relation  of  of  sub-contram/  opposition,  in  consequence 

each  other.  oi  which.  one  may  prevail  and  control  the 
Method  without  influence  from  the  others,  and  yet  no 
Method  can  be  formed  in  which  all  of  the  Ideas  can 


I.]  OF  THE  ELEMENTS  OF  METHOD. SECT.  m.  201 

be  combined,  each  in  its  perfection.  At  least,  man  in 
his  present  state  has  never  been  able  thus  to  combine 
these  ideas,  and  we  are  satisfied  with  any  object  when 
in  determining  its  method  that  idea  has  had  the  ascend- 
ency which  in  the  common  estimation  ought  to  have 
the  controlling  influence  in  such  cases.  Thus  in  an  act, 
the  moral  character  of  which  is  strongly  marked  and 
of  an  unalterable  character,  as  parental  affection,  filial 
duty,  gratitude  to  benefactors,  fidelity  to  an  engage- 
ment, Ac.,  we  are  shocked  and  indignant  if  considera- 
tions of  ./Esthetics,  or  of  expediency,  are  allowed  to 
take  precedence  of  that  controlling  influence  which 
Right  and  Good  ought  to  have  in  such  cases.  In  the 
fine  arts,  on  the  other  hand,  the  artist  entirely  fails  of 
his  object  unless  he  subordinates  all  other  considera- 
tions to  that  of  the  Beautiful.  The  same  holds  true  in 
regard  to  objects  whose  final  cause  is  Utility.  Any 
attempt  or  pretence  of  motives  of  conscience  in  matters 
which  are  indifferent  in  themselves,  as  in  the  cut  of  a 
coat,  the  color  of  a hat,  the  shape  of  a house,  &c.,  &c., 
is  but  ridiculous  fanaticism  ; just  as  any  attempt  at  the 
display  of  ornament  in  cases  where  utility  alone  is 
sought  for  is  an  offence  against  good  taste,  which  im- 
plies either  a want  of  culture  or  a want  of  sensibility. 
The  man  who  should  attempt  the  ornaments  and  plea- 
santries of  poetry  in  a mathematical  demonstration, 
would  be  considered  hopelessly  bad  in  respect  both  to 
taste  and  good  sense. 

777.  Still  however  the  Ideas  of  the  Beautiful  and 
the  Useful  are  so  related,  that  we  seldom  The  Beautiful 
pursue  the  one  without  some  regard  to  the  ;\",d  hUe  Sm- 
other. Seldom  do  we  so  far  abandon  our-  bined- 
selves  to  the  luxurious  emotions  of  delight,  awakened 
by  the  Beautiful  either  in  nature  or  in  art,  but  that 
considerations  of  economy  and  utility  come  in  for  some 
share  in  the  control  of  our  actions.  Nor  is  it  often 
that  the  iron  rule  of  necessity  so  far  breaks  down  the 
spirit  or  paralyzes  the  wings  of  the  fancy,  that  we  are 
content  with  fulfilling  the  conditions  and  recpiirements 


202 


LOGIC.— PART  II. 


[CHAP. 


of  utility  alone.  The  commonest  tool  of  the  mechanic, 
the  utensils  of  the  housekeeper,  and  even  the  imple- 
ments of  the  hoy  who  cleans  the  stables,  are  all  fash- 
ioned and  finished  with  some  regard  to  beauty  of 
shape — some  regard  to  good  looks — some  considera- 
tions of  taste. 

778.  In  most  of  the  transactions  of  life  the  desire 
The  desire  of  to  combine  as  much  of  usefulness  and  of 
of  Beauty  and  beauty  as  practicable,  is  a leading;  and  con- 
utility  combm-  p.0pqng  motiye.  In  building  a dwelling- 

house,  or  a church,  for  instance,  utility  is  the  first 
object.  But  we  often  sacrifice  something,  and  some- 
times much  of  utility,  for  the  sake  of  realizing  some 
conception  of  beauty  which  has  entered  into  our  plans. 
And  always  do  we  superadd  much  to  what  utility 
alone  would  require,  for  the  sake  of  making  our  struc- 
ture pleasing  to  the  taste.  The  same  remark  holds 
equally  true  in  regard  to  articles  of  dress,  of  furniture, 
equipage,  and  whatever  circumstances  we  may  choose 
to  surround  ourselves  with.  And  rarely  do  we  become 
so  hurried  with  business,  so  engrossed  with  care,  so 
jaded  with  over  exertion,  or  broken  with  affliction  and 
disappointment,  that  we  become  entirely  indifferent  to 
the  appearance  of  things  about  us. 

SECTION  IV. 

Of  the  Matter  of  Logical  Methods. 

779.  The  second  element  to  be  considered  as  that 

Matter  as  de-  which  determines  Method,  is  the  Matter  on 
termimng  Me-  efj?01q  or  labor  is  to  be  bestowed. 

This  must  precede  a consideration  of  the  Means,  be- 
cause different  matter  will  require  different  means. 
The  “ tools”  (which  are  but  the  Means  of  the  artisan) 
of  a shoemaker,  a hatter,  and  a stonemason,  for  in- 
stance, are  as  unlike  as  the  material  upon  which  they 
are  to  work,  and  the  Means  themselves  must  be  deter- 
mined by  the  Matter. 


I.]  OF  THE  ELEMENTS  OF  METHOD. SECT.  IV.  203 

780.  For  this  reason  we  will  hereafter  confine 

ourselves  to  the  consideration  of  those  Methods  which 
concern  the  discovery,  proof,  and  communi-  Limitalion  of 
cation  of  knowledge.  the  Subjeot- 

781.  We  have  already  reviewed  the  Matter  of  Logic 
so  far  as  the  investigation  of  the  Formulae  can  com- 
mand.* But  its  relation  to  Method  requires  a recon- 
sideration of  it  from  another  point  of  view,  and  with 
reference  to  another  end  to  be  accomplished. 

782.  When  a Judgment  affirms  of  its  Subject  only 
a property  which  was  necessarily  implied  in  the  con 
ception  of  the  Subject  itself,  the  Judgment  ^ f ^ 
is  called  an  Analytical  Judgment.  But  if  synthetiijudg- 
it  adds  to  or  affirms  of  the  Subject  a pro-  men 
perty  which  was  not  necessarily  implied  in  the  con- 
ception of  the  Subject,  the  Judgment  is  called  Synthe- 
tical. Thus,  “ Every  triangle  has  three  sides,”  is  an 
Analytic  Judgment,  we  cannot  conceive  of  a triangle 
without  three  sides.  Nor  can  we  form  a conception 
of  a triangle  at  all  without  thinking  of  its  three-sided- 
ness. Hence  Analytical  Judgments,  while  Analytical 
they  serve  to  amplify  our  knowledge  and  put  ™tsm7ncreate 
our  conceptions  into  Judgments  for  deduc-  K,‘mvIcdsc- 
tive  purposes,  do  not  increase  our  knowledge  at  all. 
But  the  Proposition,  “ The  angles  of  a triangle  are 
equal  to  two  right  angles,”  is  a Synthetic  Judgment. 
For  although  this  is  a necessary  truth,  yet  the  property 
affirmed  in  the  Predicate  is  not  a part  of  the  matter  of 
the  conception  of  a triangle,  as  is  obvious  from  the 
fact  that  we  may  know  what  a triangle  is  without 
knowing  this  property  of  triangles.  Hence  a Synthetic 
Judgment  always  adds  to  the  stock  of  our  knowledge. 

783.  An  Analytic  Judgment  affirms  of  a Subject 

only  what  was  necessarily  implied  in  the  conception 

of  the  Subject.  But  it  is  one  thing  to  be  Matter  of  the 

implied  in  the  conception  of  a Subject,  and  M°ant“rpt‘o°fn  the 

another  to  be  implied  in  the  existence  or  of  ob' 


Chap.  I.  of  Part.  I. 


204 


LOGIC. PART  II. 


[chap. 


reality  of  the  Subject ; thus,  to  take  the  example  just 
given,  “ three-sidedness ,”  is  necessarily  implied  in  the 
conception  of  a triangle.  But  “ the  equality  of  its 
angles  to  two  right  angles ,”  though  necessarily  implied 
in  the  nature  and  reality  of  the  triangle,  is  not,  as  we 
have  seen,  necessarily  implied  in  the  conception  of  it. 
A triangle  however  could  no  more  he  a reality,  that  is 
a triangle,  without  the  equality  of  its  angles  to  two 
right  angles,  than  without  its  three-sidedness. 

784.  Now  the  Matter  of  all  Judgments,  whether 
Synthetic  or  Analytic,  which  affirm  of  any  Subject 
Necessary  only  what  is  necessary  to  its  reality  as  an 

Matter.  individual  in  any  particular  genus,  is  called 

Necessary  Matter.  Or  in  other  words,  all  Judgments 
based  upon  the  principle  of  contradiction  are  in  Neees- 
Efiect  of  con.  sary  Matter.  Hence,  if  we  deny  the  Predi- 
tradiction.  cate  we  necessarily  exclude  the  Subject,  not 
from  reality,  but  from  the  genus  which  the  Subject 
denotes.  Thus  if  I predicate  of  a circle  that  its  radii 
are  not  all  equal  to  each  other,  it  may  be  a figure  and 
a curve,  but  it  is  not  a circle.* 

* There  is  no  simple  term  that  may  not  he  affirmed  as  a Predicate  of 
something  either  real,  possible,  or  impossible  in  the  abstract ; though  not 
always  in  the  concrete  (Part- 1.  279,  280).  Thus  we  may  not  always  be  able 
to  predicate  “ walldng  ” in  the  concrete  of  any  individual,  hut  in  the  abstract 
we  may  always  predicate  it  not  only  of  man  but  also  of  other  beings,  as  a 
property  which  we  conceive  as  belonging  to  them  in  posse  if  not  in  esse — Iv 
eV TeAe'xem  if  not  iv  ivtpyaa.  Hence  when  the  Predicate  is  a simple  term, 
the  Principle  of  contradiction  can  only  exclude  the  subject  spoken  of  from 
the  genus  denoted  by  the  name  given  to  it,  and  used  as  a subject  in  the 
Proposition.  As  when  we  say,  “ this  circle  has  unequal  radii,”  the  Prin- 
ciple of  contradiction,  if  applied,  would  exclude  the  figure  spoken  of  from 
the  genus  “ circle,”  though  it  might  leave  it  in  some  other  genus  of  reali- 
ties— as  the  ellipse  for  instance. 

But  we  sometimes  have  a complex  Predicate,  which,  by  the  Principle  of 
contradiction,  would  exclude  the-  Subject  not  only  from  reality  but  from 
possibility  also.  Thus  if  one  should  say,  “ this  figure  is  a two-sided  tri- 
angle,”— “two-sidedness”  and  “triangularity”  cannot  he  combined  as 
predicates  of  the  same  subject.  Hence  their  combination  produces  a com- 
plex term,  which  can  he  affirmed  of  nothing,  whether  real  or  possible,  and 
the  Proposition  affirms  no  judgment.  It  is  mere  non-sense.  It  will  ho 
found  that  the  number  of  such  that  one  meets  with  in  his  intercourse  with 
human  minds,  whether  orally  or  in  hooks,  is  vastly  greater  than  he  would 
at  first  expect. 


OF  THE  ELEMENTS  OF  METHOD. — SECT.  IY.  205 


*•] 


785.  It  is  manifest,  however,  that  Judgments  in 
Necessary  Matter  may  affirm  of  a Subject  something 
more  than  the  Essentia  of  its  conception,  judgments  in 
Most  of  the  properties  of  the  figures  with  m?cemayyaffi?m 
which  Geometry  is  concerned,  are  proper-  Sethenl“lme- 
ties  conjoined  in  some  such  way  with  the  t,a- 
Essentia  of  their  several  genera,  and  yet  they  are  not 
Essentia,  for  they  are  not  known  as  soon  as  the  con- 
ception of  the  class  is  formed.  One  knows  what  a circle 
or  an  ellipse  is,  for  instance  (so  that  he  could  never  be 
mistaken  in  deciding  with  regard  to  any  figure,  whe- 
ther it  is  a circle,  or  an  ellipse,  or  not),  long  before  he 
knows  all  the  properties  which  are  implied  in  the  very 
nature  of  those  curves. 

786.  But  if  we  pass  from  the  consideration  of  such 
matter  to  the  consideration  of  the  realities  a][  b.ectg 
of  being,  we  find  there  that  any  object  of  have  properties 

-l  ,°  i . . i not  contained 

thought  has  properties  winch  not  only  are  in  this  ciass- 
not  contained  in  its  class-conception  (as  the  concei’llon- 
Essentia  of  the  proximate  genus  has  with  propriety 
been  called),  but  which  do  not  appear  to  us  to  be  in 
any  way  necessarily  connected  with  the  matter  of  that 
conception.  Such  in  fact  are  most  of  the  properties 
of  the  objects  of  the  natural  world  ; they  con-  contingent 
stitute  what  is  called  Contingent  Matter — for  Matter- 
it  seems  to  be  contingent  or  dependent  upon  the  will 
of  the  Creator,  whether  they  should  have  such  proper- 
ties or  not.* 

* Necessary  Matter  is  that  which  is  affirmed  or  denied  on  the  Principle 
of  Identity  or  Contradiction. 

But  there  is  a class  of  philosophers  who  either  ignore  or  deny  the  dif- 
ference between  Necessary  and  Contingent  Matter.  Among  those  is  Mill, 
in  his  Logic.  Prof.  Whewell  has  affirmed  the  distinction  on  two  grounds  : 

(1.)  That  Necessary  Judgments  affirm  what  has  never  been  a matter 
of  experience,  as  when  we  say,  “ Two  straight  fines  can  never  inclose  a 
space.” 

To  this  Mr.  Mill  replies,  that  what  we  can  construct  in  the  imagination 
is  as  much  a matter  of  experience  as  that  which  we  may  have  seen  in  the 
reality  of  being.  We  can  imagine  two  straight  fines  infinitely  extended, 
and  yet  not  inclosing  a space. 

(2.)  Prof.  Whewell  said  also  that  the  Judgments  which  we  call  Neces- 


206 


LOGIC. — PART  II. 


[chap 


787.  Now  all  Judgments,  whether  analytical  or 

judements  in  synthetic,  in  Necessary  Matter  are  called 
ter  a priori.  Judgments  a prion  ; that  is,  Judgments 
which  are  affirmed  from  a consideration  of  what  was 
contained  or  necessarily  implied  in  the  very  conception 
judgments  in  of  the  object.  But  all  Judgments  in  Con- 
conungentfliat.  tingent  Matter  are  called  Judgments  a pos- 
0Ti-  teriori  • that  is,  Judgments  which  are  and 

can  be  known  to  be  true  only  posterior  to  and  after  an 
acquaintance  with  the  Subject  as  existing  among  the 
realities  of  being. 

788.  Necessary  Matter,  therefore,  consists  of  the 
conceptions  of  realities  of  truth  ; and  Contingent  Mat- 
Nenessaryand  ter,  in  what  is  added  thereto  to  constitute 

to  nin"  the ‘same  them  realities  of  being.  Thus,  suppose  I 
conception.  form  a conception  of  a point  in  space — as  a 
point  it  has  no  extension.  It  is  a reality  of  truth  hut 
not  of  being.  I conceive  that  point  to  move  directly 
towards  another  point  in  space  — the  path  which  the 
point  is  thus  conceived  to  describe,  I call  a straight 

sary,  differ  from  the  Contingent  in  that  we  cannot  even  imagine  or  con- 
ceive of  an  exception  to  the  Necessary,  whereas  all  Contingent  Propositions 
actually  have  exceptions. 

But  Mr.  Mill  replies,  that  this  rather  proves  the  limited  capacity  of  our 
powers  than  any  thing  else.  Many  things  have  now  become  true  which 
not  long  ago  were  not  and  could  not  have  been  conceived  as  true  or  pos- 
sible. 

Without  deciding  upon  the  merits  of  this  controversy  thus  waged,  I will 
add  for  the  consideration  of  those  who  think  with  Mr.  Mill,  that  all  men 
perceive  a difference  in  the  kind  of  certainty  which  they  feel  in  the  truth, 
that  “ every  triangle  has  three  sides  ; ” and  those  Contingent  Propositions 
which  we  are  continually  offering.  Thus  I say,  “ The  rose  is  red — the 
apple  is  unripe — the  horse  is  gray — that  man  has  ten  fingers,” — every  body 
sees  that  the  one  may  have  ten  fingers  and  yet  be  a man,  that  a horse  may 
cease  to  be  gray  without  ceasing  to  be  a horse,  that  an  apple  may  be  un- 
ripe, or  a rose  yellow.  But  if  the  (so  called)  triangle  has  not  three  sides, 
it  is  miscalled,  it  is  no  triangle,  and  the  Proposition  cannot  be  true.  Change 
the  quality  of  the  Copula  and  you  destroy  the  Logical  Essentia  of  the  Sub- 
ject. But  in  the  other  examples  given,  this  change  in  the  quality  of  the 
Copula  may  be  made  without  changing  the  Essentia  of  the  Subject  at  all, 
and  thus  causing  it  to  cease  to  be  of  the  species  to  which  by  its  name  we 
had  referred  it.  No  one,  I suppose,  will  deny  the  difference  thus  pointed 
out  between  those  two  classes  of  Judgments — we  make  it  a Differentia  of 
the  Species,  the  one  Nocessary  and  the  other  Contingent  Judgments. 


I.]  OF  THE  ELEMENTS  OF  METHOD. SECT.  IV.  207 

line — the  line  also  is  only  a reality  of  truth.  I suppose 
the  point  to  move  again  towards  another  point  not  in 
that  straight  line.  It  generates  another  straight  line. 
I conceive  it  to  move  again  directly  to  the  point  from 
which  it  started.  It  has  now  generated  a third  line  in 
such  a relation  to  the  other  two  as  that  it  joins  them,  and 
they  then  make  a triangle.  The  triangle  is  a reality  of 
truth ; and  I conceive  of  it,  that  is,  have  a conception 
of  it,  as  a figure  with  three  straight  sides,  including 
three  angles.  These  two  properties  are  the  matter  of 
my  class-conception.  From  this  I deduce  A priori  de. 
a priori  the  further  property,  that  the  sum 
of  its  angles  are  just  half  as  much  as  the  ception- 
sum  of  all  the  angles  that  can  be  formed  around  any  one 
point  in  space  ; and  that  if  I know  the  size  of  any  one 
of  its  angles  and  the  two  adjacent  sides,  or  if  I know 
the  length  of  one  side  and  the  size  of  the  two  adj  acent 
angles,  I can  determine  the  size  of  the  other  angles 
and  the  length  of  the  other  sides.  In  the  same  way,  I 
may  construct  in  my  mind  a rectangle,  a circle,  an 
ellipse,  &c.,  and  of  each  I can  ascertain  a priori,  many 
properties  which  did  not  enter  into  the  class-conception 
of  those  figures. 

789.  But  if  I take  up  my  crayon,  before  a black- 
board, and  make  a dot,  calling  that  a point, 
and  make  a mark  as  straight  as  I can,  call-  tion  drau°nmpa 
ing  that  a line,  &c.,  these  figures  on  the  D,asrdm’ 
board  are  not  the  realities  of  being  of  which  I had 
formed  the  conception,  and  of  which  I had  demon- 
strated, or  of  which  I could  demonstrate  those  propo- 
sitions. These  marks  may  represent , but  they  are  not 
the  point,  the  line,  the  triangle,  &c.  I can 
predicate  much  of  those  marks  that  could  predated"  or 
not  be  predicated  of  the  realities  of  being  than0ftheco“ 
which  they  represent.  Thus  the  mark  has  ception' 
breadth,  the  line  none — the  mark  has  color,  and  is 
upon  a ground  of  a different  color — a white  mark  on  a 
blackboard,  for  instance ; the  line  has  no  such  pro- 
perties. These  realities  of  truth,  the  point,  the  line,  &c., 


208 


LOGIC. — PAJBT  II. 


[CHAP. 


have  been  done  or  made  into  facts — realities  of  being  in 
the  outer  world.  They  have  been  clothed  upon  with 
visible  forms,  having  properties  of  their  own  in  addition 
to  those  contained  in  their  class-conception.  Now  all 

, . these  properties  are  Contingent  Matter.  It 
in  contingent  depends  upon  my  will  whether  I will  give 
to  my  conception  of  a triangle  an  outward 
expression  on  the  blackboard  or  not ; and  whether  that 
expression  shall  be  with  a white  mark  or  a mark  of 
another  col  Or ; whether  the  mark  shall  be  small  and 
smooth,  or  broad,  rough,  and  irregular,  &c. 

790.  Let  us  pass  to  another  class  of  objects.  Sup- 
creation.  pose  the  Divine  Mind  to  have  constructed  a 
conception  or  an  idea  of  the  various  classes  of  beings 
included  in  the  Creation.  As  existent  substantial  reali 
ties  each  individual  must  consist  of  Matter,  extended 
so  as  to  fill  limits  in  space  and  to  be  impenetrable  ; 
be  composed  of  particles,  every  one  of  which  should 
have  an  attraction  for  every  other  particle,  and  this  sub- 
stantial matter  must  be  without  life  or  capacity  of 
originating  motion  or  of  acting,  except  as  it  was  acted 
upon  by  a spirit  either  within  or  from  without  each 
i lividual  object. 

791.  Now,  here  we  have  the  class-conception  of  the 
objects  which  have  a material  existence.  From  this  we 
a priori  infer-  can  deduce  a priori  many  of  the  funda- 
conceptio”  ‘of  mental  principles  of  the  Natural  Sciences. 
Matter.  From  extension  must  follow  the  divisibility'' 
of  all  material  objects ; from  attraction  must  follow 
density  and  the  phenomena  of  gravitation  ; from  in- 
ertia the  three  laws  of  motion  may  be  deduced,  and 
so  on.  We  should,  however,  know  nothing  of  the 
phenomena  of  light,  of  color,  of  electricity,  of  sound, 
of  chemical  combination,  &c.,  from  these  mere  class- 
conceptions. 

792.  But  let  this  Divine  Conception  pass  into 
contingent  reality  of  existence — be  done  into  a fact, 

saniy r impifed  and  each  piece  of  matter  necessarily  takes 
of  be!ng.real,ty  upon  itself,  or  rather  its  Creator  puts  upon 


I.]  OF  THE  ELEMENTS  OF  METHOD.. — SECT.  IV.  209 

it  properties  and  relations  not  implied  in  the  class- 
conception  or  resulting  therefrom ; but  which  are, 
however,  necessary  to  the  reality  of  each  individual 
object  among  the  facts  of  existence.  The  specific  color 
and  shape  of  each  piece  of  matter,  for  instance,  though 
it  must  have  some  color  and  shape,  were  to  be  deter- 
mined by  the  will  of  the  Creator,  and  not  necessarily 
implied  in  the  conception  or  the  resolution  to  give  it 
reality  of  being.  Those  properties  of  the  outward  form 
of  the  conception — its  material  body — are  contingent  Mat- 
like the  diagrams  by  which  we  represent  ter  how  known, 
our  conceptions  of  a triangle,  a pyramid,  &c.,  matters 
of  choice  and  chosen  by  ourselves,  and  can  never  be 
known  by  any  other  mind  until  he  has  learned  them 
either  by  revelation — that  is,  verbal  communication 
from  ourselves,  or  by  an  inspection  and  study  of  the 
diagram  which  we  have  drawn. 

793.  From  the  foregoing  considerations  of  the  Mat- 
ter of  Judgments,  we  may  divide  the  Pro-  a new  classic- 

a % . , . d n f?  . cation  of  Pro- 

perties ot  Objects  again  with  reference  to  penies. 

Method  on  another  principle  and  into  other  classes. 

794.  Thus  all  of  those  Properties  which  are  in- 
cluded in  the  class-conception  may  be  called  Materiai  Pro. 
Material  Properties  y as  three-angledness  and  perties- 
three-sidedness  of  a triangle,  extension  and  inertia  in 
matter,  &c.  Then  all  of  those  Properties  which  are 
necessarily  implied  in,  and  deducible  a priori  from 
these  Material  Properties  may  be  called  the  Implied 
Properties,  as  the  equality  of  the  angles  of  a Implied  Pro. 
triangle  to  two  right  angles,  divisibility  from  perties- 

the  extension  of  matter,  and  the  laws  of  motion  from 
its  inertia. 

795.  Those  properties  of  bodies  which  serve  to 
make  the  species  of  objects  in  the  reality  of  Pr0Perties  0f 
being,  such  as  two-footedness  of  man,  canine  h‘kgremay  be 
teeth  or  the  carnivora,  web-footedness  of  matcria1' 
aquatic  birds,  unsupportedness  of  falling  bodies,  &c., 
may  indeed  be  assumed  as  Material  Properties  in  our 
conception  of  the  class,  and  as  such  we  may  reason 


210 


LOGIC. — PART  n. 


[chap. 


from  them  a priori  to  other  implied  properties,  just 
as  from  the  three-angledness  of  a triangle  in  Mathe- 
matics. 

796.  But  for  the  most  part,  and  always  for  all  the 
purposes  of  science,  these  properties  are  learned  a pos- 

. . teriori , from  actual  observation  of  the  indi- 
dicaTiv"  "of  "a  viduals  existing  in  the  reality  of  being. 

Final  Cause.  7r,  , , , ° , . , J & 

Jiacli  ot  these  properties,  however,  is  con- 
nected with  and  is  suggestive  of  a Final  Cause,  for 
which  it  was  bestowed  upon  individuals  of  that  class  ; 
the  two-footedness  of  man  was  designed  as  a means  to 
the  upright  position  in  which  he  walks  ; and  so  through- 
out the  material  world  we  connect  those  properties 
which  are  differentia  of  species  with  something  in  the 
habits  or  modes  of  the  individuals  of  the  species,  as 
two-footedness  with  erectness  of  stature — canine  teeth 
with  carnivorQusness,  &c. 

797.  Flow  in  reference  to  this  fact  we  may  call  the 
can  Formal  former  Properties  which  are  indicative  of 

properties.  tli e Final  Cause  the  Formal  Properties  ; 

and  those  which  are  thus  connected  with  them  and 
Modal  pro-  implied  in  their  reality,  we  may  call  the 
perties.  Modal  Properties.  And  all  those  Proper- 
ties which  are  susceptible  of  more  and  less,  as  size , 
variable  pro-  temperature , density , might , &c.,  we  may 
perties.  Call  variable  Properties. 

798.  It  will  be  observed  that  Material  and  Formal 
Material  and  are  ii ot  coordinate  terms,  but  only  terms 
ordmat e "te rms*  denoting  alternate  conceptions.  Material 
and  Implied  are  the  coordinates  in  a priori  Matter. 
Formal  and  Modal  are  the  coordinates  in  a posteriori 
Accidental  and  Matter.  Then  besides  these  we  have  the 
pe«ies maybe-  Accidental  and  Variable  Properties.  These, 
Material  "'“of  however,  may  become  either  Material  or 
Formal.  Formal.  But  when  they  do  become  so  they 
cease  so  far  forth  as  they  are  Material  or  Formal  to  be 
accidental  to  the  individuals  into  wdiose  class-concep- 
tion they  have  thus  entered.  Thus,  the  “ unsupport- 
edness ” of  bodies  which  fall  is  but  an  accidental 


I.J  OF  THE  ELEMENTS  OF  METHOD. SECT.  IV.  211 

property  of  those  bodies  as  masses  of  matter.  But 
we  assume  it  as  a Formal  Property  with  reference  to 
the  Modal  Property  denoted  by  the  word  “falling 
when  we  say  that  “ all  bodies  which  are  unsupported, 
fall  to  the  ground.”  So  too  “ right-angledness  ” is  but 
accidental  to  “ triangle ; ” but  when  we  take  it  into 
our  class-conception  we  have  “ right-angled  triangles,” 
and  then  it  becomes  Material. 

799.  Now  as  the  Matter  of  all  a priori  Judgments 
is  necessary  Matter,  if  the  Judgment  be  af-  Contra 
firmative,  its  contrary  or  contradictory  is  dictory or j"dg- 

n , . ' 7 7.,  ^ t,  • , -i  ments  in  Neces- 

called  an  absurdity.  It  is  not  merely  an  sary Matter  ab- 

i/  i/  curd 

error.  Of  this  kind  are  all  mathematical 
and  all  analytic  Judgments.  If  the  Judgments  be 
negative,  the  affirmative  would  give  a nihil  pururn — - 
that  is,  an  impossibility  ; as  that  two  and  two  make 
five,  two  straight  lines  may  inclose  a space,  an  effect 
without  a cause. 

800.  In  Necessary  Matter  if  the  subaltern  is  true, 
its  universal  must  be  true  also.  That  is, 

It  I IS  true  A must  be  true  also.  ferences  from 

If  O is  true  E must  be  true  also.  Nere“a?^Matn- 

And  all  contraries  are  virtually  contradic- 
tories, and  only  one  of  the  sub-contraries  I and  O can 
be  true. 

801.  Contingent  Matter  is  also  divided  into  Natural 
and  Moral. 

Although  the  order  of  Nature  seems  to  be  per- 
fectly stable  and  uniform,  we  conceive  this  order  as 
having  been  established  by  an  Intelligent  Knowledge 
Author  as  the  choice  of  His  will.  In  many  Matteronoinpe<w- 
respects  we  can  conceive  of  it  being  differ-  tKriorL 
ent  from  what  it  is,  and  for  the  most  part  we  know 
nothing  of  its  facts,  principles,  or  laws  until  we  have 
observed  and  studied  them  from  actual  facts  and  oc- 
currences. Hence  clearly  the  knowledge  of  Nature  is 
a posteriorf  and  the  Matter  itself  is  contingent. 

802.  But  so  great  is  the  uniformity  and  constancy 
of  its  operations  and  processes,  that  we  consider  its 


212 


LOGIC. — PART  n. 


[chap. 


laws  as  almost  as  certain  as  the  deductions  of  mathe- 
physicai  cer  matics  themselves.  But  the  certainty  is  not 
lamty.  quite  so  great  (since  there  always  may  be 

exceptions),  and  it  is  different  in  kind.  Hence  we  call 
it  a physical  certainty.  And  the  contradictory  of  any 
proposition  enunciating  a physical  truth  or  certainty 
would  not  he  an  absurdity,  but  simply  a falsehood  or 
error. 

803.  But  in  the  actions  of  man  there  is  no  such 
uniformity  as  we  find  in  Nature.  His  moral  freedom 
Moral  Matter,  places  his  acts  at  the  disposal  of  his  will, 
rather  than  of  any  law  which  operates  uniformly  in  all 
similar  cases. 

804.  Hence  in  the  actions  of  man  there  is  not  a 
necessity  of  any  kind,  in  the  proper  sense  of  the  word. 
Since,  however,  the  will  of  man  is  influenced  in  some 
measure  by  motives  external  to  itself,  any  strong  com- 
Morai  and  phy-  bination  of  motives  will  usually  induce  a 
sicai  Necessity,  particular  kind  of  action ; and  hence  this 
class  of  actions  are  said  to  constitute  a sort  of  moral 
necessity.  The  objects  in  Nature  are  not  conceived  as 
having  any  liberty  to  choose  what  they  will  do,  or  any 
power  to  act  except  as  they  are  acted  upon. — Hence 
the  physical  necessity.  On  the  other  hand,  man  is 
conceived  as  having  the  power  to  choose  what  he  will 
do,  to  act  in  accordance  with  external  forces  or  against 
them  ; and  hence  his  acts  are  not  under  the  same  law 
as  that  which  determines  the  motions,  the  facts,  and 
events  in  Nature. 

805.  Still,  however,  there  is  some  uniformity  in  the 

acts  of  men  under  similar  circumstances  ; and  hence  a 
knowledge  of  the  circumstances  always  gives  a strong 
Moral  certain-  ‘probability  as  to  the  course  one  will  pursue. 
ty-  This,  when  it  exists  in  but  a low  degree, 

is  called  merely  probability.  But  when  the  proba- 
bility becomes  very  great,  it  is  called  a moral  cer- 
tainty. 

806.  The  same  principles  are  also  extended  to  the 
events  of  Providence  ; that  is,  future  events  which  are 


I.]  OF  THE  ELEMENTS  OF  METHOD. — SECT.  IV.  213 

not,  so  far  as  we  know,  under  the  control  of  any  phy- 
sical laws  and  causes,  but  which  are  sup-  Mora,  Cer. 
posed  to- depend  upon  the  overruling  Provi-  Ih'J1  ayc t B°of h-ro" 
dence  of  God.  What  the  probability  lacks  vidence- 
of  certainty  in  the  two  cases,  however,  depends  upon 
two  entirely  different  grounds.  In  the  case  of  man  it 
depends  upon  the  fact  that  he  does  not  always  act 
consistently  with  himself,  or  as  he  ought.  But  in  the 
case  of  the  acts  which  are  conceived  as  depending  upon 
the  will  of  God,  the  uncertainty  in  our  minds  arises 
solely  from  our  not  understanding  His  ways,  and  the 
laws  and  principles  upon  which  He  acts  in  His  govern- 
ment of  the  world. 

807.  There  are  some  cases,  however,  in  which  even 
man  may  acquire  such  a character,  as  that  circumstances 
we  feel  a certainty  as  great,  though  different  i""eaofSMorhal 
in  kind,  as  though  it  were  absolute  with  Certa,nty' 
regard  to  the  course  he  will  pursue.  We  know  that 
Washington  will  be  patriotic,  Hey  will  he  brave, 
Howard  benevolent,  and  that  St.  Paul  will  hesitate  in 
view  of  no  peril  to  himself  in  doing  what  he  regards 
as  the  will  of  God. 

808.  So  too  in  forecasting  the  conduct  of  masses 
of  men,  we  can  calculate  with  almost  a phy-  Certainty  in 
sical  certainty — almost  as  surely  as  the  mo-  Suet10  lof 
tions  of  the  heavenly  bodies.  Masses  can  “asses  of  men. 
never  differ  from  one  another  so  much  as  one  indi- 
vidual may  differ  from  another.  Hay,  when  masses 
become  quite  large,  the  Political  Economist  and  the 
Statesman  can,  from  knowledge  of  the  circumstances, 
determine  beforehand  in  general  terms  what  course 
men  will  pursue,  and  what  result  they  will  arrive  at, 
almost  as  certainly  as  the  astronomer  can  determine 
the  return  of  a comet. 

809.  The  Matter  which  thus  determines  Logical 
Methods  admits  of  being  resolved  into  several  ele- 
ments, to  which  we  will  refer  for  a moment,  in  order 
to  get  a little  more  distinct  conception  of  them. 

810.  Every  object  of  thought,  regarded  merely  as 


214 


LOGIC. PART  II. 


[CHAP. 


an  object  about  which  our  thoughts  are  occupied, 
and  over  the  existence  of  which  in  the  past  and  in  the 
Facte.  present  we  have  no  control,  may  be  regarded 

as  a fact.  Thus,  what  one  has  been,  said,  or  done, 
and  even  the  intention  of  that  which  was  intended  but 
left  undone ; whatever  exists  or  has  existed,  whether 
in  the  mind  alone  or  embodied  in  some  external  form, 
is  a fact. 

811.  The  word  “fact”  is  from  facio,  to  do,  and  is 
used  with  reference  to  something  done , or  something 
which  has  been  brought  into  the  reality  of  exist- 
ence. 

812.  We  distinguish  a fact  from  an  event  by  apply - 

Event.  ing  the  word  “fact  ” to  that  which  remains 

as  the  result  of  the  making.  But  by  an  “ event”  on 
the  other  hand,  we  mean  the  happening  or  occurring 
itself,  even  if  it  leaves  no  fact,  or  factum , thing  done, 
behind.  But  an  “ event  ” is  the  mere  happening,  it  is 
a mere  phenomenon;  it  appears  in  time,  is  instanta- 
Events  pass  in-  neous,  and  then  ceases.  Hence  the  same 
to  Facts.  thing  may  be  regarded  as  both  a fact  and 
an  event ; the  birth  of  Napoleon,  for  instance,  was 
both  an  event  and  a fact.  As  an  event,  it  happened 
or  occurred  on  a certain  day,  at  a certain  hour  and 
moment — was  real  as  an  event  then  and  then  only. 
But  as  a fact,  a thing  done — a thing  that  is  remem- 
bered, enters  into  and  forms  a part  of  history,  it  is  as 
real  now  as  it  ever  was,  and  must  remain  so  forever. 

813.  Again,  we  distinguish  “ facts  ” from  mere 
Facts  distin-  realities  of  truth.  A point,  a line,  a triangle, 

Conceptions.  would  hardly  be  called  facts  ; they  are  rather 
realities  of  truth  than  of  being,  of  which  the  mind  forms 
conceptions  by  means  of  its  own  activity.  The  dot, 
the  mark,  &c.,  are  not  points  and  lines,  they  only  re- 
present them. 

814.  We  also  distinguish  “facts”  from  Ideas.  We 
Facts  distin-  could  hardly  speak  of  time,  of  space,  of 

fdcased  lrom  cause,  of  substance,  of  truth,  as  facts.  We 
do  not  conceive  of  them  as  made,  but  rather  as  neces- 


I.J  OF  THE  ELEMENTS  OF  METHOD. — SECT.  IV.  215 


sary  and  eternal  realities  anterior  to  any  act  of  creation, 
any  act  of  making  or  conceiving  them. 

815.  We  distinguish  *“  facts”  from  “fancies”  or 
“phantasms”  also.  The  facts  are  supposed  ^ dj3tjn 
to  have  an  objective  reality  of  Being.  The  guished  from 
phantasm  or  fancy  has  none.  It  is  a mere 
combination  of  properties  in  the  mind,  to  form  that 
which  is  the  representation  of  nothing  that  exists  or  is 
supposed  to  exist. 

816.  Any  facts  which  attend  upon  or  surround 
another  fact  as  their  principal  are  called  circumstances. 
circumstances. 

817.  Facts,  as  they  first  become  objects  of  thought, 
are  complex  wholes.  We  do  not  perceive  Fact9  at  first 
color,  size,  shape,  density,  &c.,  each  sepa-  complex- 
rately  and  one  after  the  other ; and  then  combine  them 
by  any  conscious  or  voluntary  operation  into  the  per- 
ception of  an  object.  But  we  perceive  the  object  as 
a whole,  and  then  by  an  act  of  reflection  we  consider 
these  properties  separately. 

818.  The  process  by  which  we  resolve  the  per- 
ceived whole  into  its  parts  is  called  Analy-  Analysis, 
sis  ; and  the  act  of  considering  one  of  the  parts  alone, 
and  by  itself  is  called  Abstraction  / and  the  Abstraction, 
name  by  which  the  part  is  thus  designated  is  called  an 
abstract  term. 

819.  Analysis  has  different  methods  in  different 
kinds  of  matter ; thus  the  chemist  has  one  Different  kinds 
kind  of  Analysis,  the  mathematician  another,  ot  Analys,s- 
and  the  metaphysician  another.* 

* “ St.  John  Damascene  says  there  are  three  kinds  of  Analysis ; the 
first  resolves  compounds  into  their  simple  elements ; the  second  resolves  the 
syllogism  into  its  several  parts  ; and  the  third  or  mathematical,  consists  in 
admitting  the  correctness  of  a certain  principle  in  order  to  arrive  at  the 
knowledge  of  an  important  truth.” — Blakey’s  Hist,  of  Int.  Philosophy , vol.  I. 
p.  274. 

Pappus,  a mathematician  of  Alexandria,  A.  D.  400,  and  author  of 
“ Mathematical  Collections,”  says  in  the  preface  to  his  seventh  book  : — 
“ Analysis  is  the  course  which  setting  out  from  the  thing  sought,  and  which 
for  the  moment  is  taken  for  granted,  conducts  by  a series  of  consequences 


216 


LOGTO. PAJRT  II. 


[CHAP. 


820.  Logical  Analysis,  of  which  alone  we  are  now 
Logical  Analysis,  speaking,  consists  in  resolving  the  concep- 
tion of  any  object  of  thought  into  those  elementary 
parts  which  go  to  make  up  the  adequate  conception 
of  that  object.  The  Analysis  is  called  proximate  when 
proximate  An-  the  parts,  any  or  all  of  them,  admit  of  further 
aiysis  & parts,  analysis.  Tims  the  Analysis  of  the  concep- 
tion of  any  object  into  substance,  attributes,  and  modes 
is  proximate.  For  the  attributes  and  modes  admit  of 
further  analysis.  But  when  the  Analysis  can  go  no 
further,  because  there  is  no  part  that  admits  of  further 

Last  or  uiti-  analysis,  it  is  called  the  last  analysis,  and 
mate  Analysis,  the  parts  given  out  by  it  are  called  ultimate 
parts.  Thus,  I analyze  my  conception  of  a piece  of 
gold  before  me  into  the  substance , which  I will  call 
gold  ; the  properties,  which  I will  call  extension,  yel- 
low, ductile,  &c. ; and  into  the  modes,  as  polished,  coin, 
ornament,  utensil,  &c.,  &c. 

821.  By  a process  which  is  the  reverse  of  Analysis, 
synthesis.  called  Synthesis,  we  put  together  these  ulti- 
mate elements  to  construct  the  complex  whole.  Thus, 
as  by  analysis  the  chemist  reduces  water  to  oxygen 
and  hydrogen,  so  by  synthesis  he  puts  these  elements 
together  and  combines  them  into  water  again. 

822.  So  also  in  Logical  Synthesis  we  put  together 
in  the  unity  of  consciousness  the  elements  of  which  a 

synthesis  of  conception  is  composed,  and  form  the  con- 
conceptions.  ception.  It  is  by  this  process  of  analysis 
and  synthesis  that  a conception  passes  from  one  mind 
to  another.  Again,  with  the  substance  for  subject  and 
any  one  of  the  properties  or  modes  for  a predicate,  we 


to  something  already  known,  or  placed  among  the  number  of  principles  ad- 
mitted to  he  true.  By  this  method,  therefore,  we  ascend  from  a truth  or 
a proposition  to  its  antecedents  ; and  we  call  it  Analysis  or  resolution,  as  if 
indicating  an  inverted  solution.  In  Synthesis,  on  the  contrary,  we  set  out 
from  the  proposition,  which  is  the  last  in  the  Analysis.”  In  the  method  of 
Analysis,  “ If  the  result  is  true  the  proposition  which  we  assumed  at  the 
outset  is  true  also,  and  the  direct  demonstration  is  obtained  [synthetically] 
by  stating  in  an  inverse  order  the  different  parts  of  the  Analysis.  If  the 
ultimate  consequence  is  false  the  proposition  was  false  also.” 


X.]  OF  THE  ELEMENTS  OF  METHOD. SECT.  IV.  217 

unite  them  into  a judgment ; these  judgments  we  com- 
bine into  a syllogism,  &c.  And  a set  of  judgments 
combined  into  a whole  by  means  of  the  unity  of  their 
several  subjects  is  called  a “System.”  The  system, 
word  is  from  a root  of  similar  import  as  “ synthesis.” 

823.  ISTow  when  the  evidence  or  grounds  upon 
which  any  system  is  based  is  such  as  to  leave  no  doubt 
of  its  truth,  as  in  mathematics,  we  call  it  a truth  or  the 
truth.  But  if  its  truth  be  still  doubtful,  and  Truth, 
received  by  those  who  accept  it,  on  grounds  which  are 
not  satisfactory,  or  not  generally  acknowledged  as  such, 
we  call  it  an  Opinion.  Truth  is  supposed  to  opinion, 
rest  upon  grounds  which  are  entirely  independent  of 
choice,  passion,  prejudice,  or  any  wishes  or  feelings  of 
a personal  character.  Opinion,  on  the  other  hand,  is 
always  supposed  to  be  indebted  for  its  reception  in 
some  measure  to  the  good  will  or  wishes  of  those 
who  hold  it ; that  is,  they  hold  it  from  choice  in  part 
at  least,  and  not  altogether  from  the  unbiassed  convic- 
tions of  their  own  judgments,  or  the  necessary  laws  of 
belief. 

821.  When  any  system  of  judgments,  or  a judg- 
ment singly  is  regarded  as  explaining  a fact  or  a series 
of  them,  it  is  called  a Theory.  Thus  we  have  Theory, 
the  facts  of  bodies  falling  to  the  earth  ; and  we  have 
the  theory  of  gravity — namely,  that  the  Earth  attracts 
them.  But  the  agency  or  efficacy  here  attributed  to 
the  Earth  is  a mere  theory.  It  may  be  consistent  with 
the  facts.  But  it  is  after  all  a theory,  and  a theory 
only.  We  have  theories  of  light,  theories  of  electri- 
city, &c. ; that  is,  some  explanation  of  the  facts,  which 
goes  beyond  the  facts  themselves,  and  serves  to  give 
them  a scientific  unity  and  completeness  ; and  it  is 
sometimes  the  case  that  the  facts  remaining  precisely 
the  same,  two  or  more  theories  will  each  of 
them  explain  the  facts  so  far  as  they  are  at  ries  for  the 
present  known  as  well  as  the  other.  This  I *dmc  lda!" 
believe  to  be  the  case  with  regard  to  the  two  theories 
of  light — the  emanation  and  the  undulation  theories  ; 

10 


218  LOGIC. — PART  n.  [chap. 

and  tlie  two  theories  of  electricity — the  theory  of  a sin- 
gle fluid  and  the  theory  of  two  fluids. 

825.  When  before  we  have  facts  enough  to  form  a 
theory,  we  guess  at  what  the  true  theory  or  explana- 
conjecture.  tion  of  the  facts  will  be — this  guess  is  called 
a Conjecture. 

826.  From  the  foregoing  definition  it  is  evident 

Analysis  pm-  that  the  collection  and  analysis  of  the  facts 
sis.  must  always  precede  m the  order  ot  a cor- 

rect method,  the  synthesis  or  putting  them  together 
into  a system,  or  combining  them  for  the  construction 
of  a theory  or  an  argument. 

827.  But  as  the  accumulation  and  careful  analysis 
of  facts  is  slow,  men  often  desire  to  construct  a 
theory  or  system  before  this  preparatory  work  has 
Hypothesis.  been  done.  In  this  case  they  are  often  com- 
pelled to  guess  at  what  the  fact  would  be  if  it  were 
known.  Such  a guess  is  called  a Hypothesis , or  some- 
thing placed  under  to  support  our  theory  or  system. 

Our  subject  will  henceforth  divide  itself  into  the 
Division  of  the  four  chief  parts — (1)  Methods  of  Investiga- 
subject.  tion  ; (2)  Methods  of  Proof ; (3)  Methods  of 
Disproof  or  Refutation  ; and  (1)  Methods  of  Instruction. 

828.  These  subdivisions  of  the  present  part  of  our 
These  parts  m-  Treatise  are  rather  alternate  than  coordinate 
than  coordi-  parts.  Ihere  is  no  investigation  that  does 

not  carry  with  it  some  conviction  of  the  cer- 
tainty of  its  result ; that  is,  some  kind  and  amount  of 
proof.  So,  too,  there  is  no  method  of  proof  that  is  not 
in  some  measure  an  investigation  into  the  truth  of  what 
it  undertakes  to  prove.  Disproof  is  of  course  a method 
of  proof.  And  Instruction,  or  the  construction  of  the 
things  known  into  systems  and  sciences,  implies  some- 
thing of  investigation  and  proof. 

Still,  however,  a division  seems  to  be  desirable  ; 
and  I shall  refer  the  various  methods  and  topics  to  one 
principle  of  or  another  of  the  four  class  terms,  accord- 
ciassiiication.  jng  as  that  which  I have  announced  as  the 
leading  subject  in  each,  is  or  is  not  the  prominent  trait 
in  the  Method  to  be  discussed. 


n.J 


METHODS  OF  INVESTIGATION. — SECT.  I. 


219 


CHAPTER  H. 

METHODS  OF  INVESTIGATION. 


SECTION  I. 

Of  Investigation. 

829.  I remarked  in  Part  I.  [451],  that  where  the 
Question  is  concerning  the  Copula,  it  is  to  be  answered 
by  some  one  of  the  Formulas.  The  Formula,  however, 
presupposes  all  the  Terms  as  given.  In  the  case  of 
Immediate  Inference,  as  well  as  in  all  Intuitive  Judg- 
ments, there  is  no  Term  needed  except  those  which 
appear  in  the  Judgment  or  Conclusion  itself.  Necessity  for 
But  we  may  often  have  a Judgment  to  be  finding  Term3- 
proved,  with  no  Exposita  from  which  it  can  he  deduced 
by  Immediate  Inference,  and  no  Middle  Term  given 
by  means  of  which  it  can  be  proved  as  a Deductive 
Judgment.  Hence  we  may  have  occasion  to  find  a 
Middle  Term.  And  in  all  cases  where  the  Question 
is  concerning  the  Major  Term  that  Term  is  still  to  be 
found. 

830.  The  finding  of  these  Terms  is  what  we  call 
Investigation •*  Whether  the  Term  to  be  sought  be  to 

* The  subject  which  we  treat  in  this  Chapter  is  to  a considerable  ex- 
tent the  same  as  that  which  Aristotle  and  the  ancients  generally  treated 
under  the  head  of  “ Topics"  or  “Loci;”  for  the  reason,  as  Mansel  ob- 
serves, that  “ it  is  the  place  in  which  we  look  for  Middle  Terms.”  Instead 
of  the  place  where  we  may  find  them,  I have  made  it  a Treatise  on  the  Methods 
of  finding  them. 

Of  these  lod  the  Schoolmen  made  two  classes : “ Marimm  ’’—that  is, 


220 


LOGIC. PAST  n. 


[chap. 


be  used  as  Middle  Term  or  not,  it  must  be  found  as  a 
. investigation  Predicate  to  the  subject  of  our  inquiry.  In  the 
predicates1.' 8 0 Methods  of  Investigation,  therefore,  Ave  are 
seeking  some  term  which  we  may  predicate  of  a given 
subject ; and  if  we  wish  to  use  it  as  a Middle  Term  to 
establish  a Copula,  it  must  be  such  an  one  as  can  be 
used  as  subject  to  that  Term  which  we  wish  to  affirm 
as  Predicate  of  it  as  Major  Term.  Thus,  if  we  wish  to 
prove  that  S is  P,  we  must  find  a Term  as  M,  which 
we  can  predicate  of  S (S  is  M),  and  of  which  we  can 
predicate  P,  as  M is  P,  and  we  then  can  affirm  our 
conclusion  S is  P in  the  First  Figure. 

831.  The  point  then  in  which  all  the  Methods  of 
potar common  Investigation  unite  is  this:  that  they  are 

ot' Investigation.  Methods  of  finding  Avhat  may  be  predicated 
of  any  given  subject. 

832.  Methods  of  Investigation,  therefore,  always 
presuppose  the  subject  to  be  given  ; that  is,  Ave  must 
subjects  given  have  something  to  investigate  ; and  we  may 
only11 16  f,plu're  have  it  given  by  its  sphere  only,  or  by  the 
matter  of  its  class-conception  determining  its  sphere. 
Thus  I may  remember  that  something  occurred  with- 
out  remembering  what  it  Avas  [52,  53].  I may  know 
that  there  is  something  in  a given  room  or  place  Avith- 
out  knoAving  Avhat  it  is  ; that  is,  I have  the  sphere  of 
the  conception  only. 

833.  In  this  case  the  first  thing  is  to  learn  what  the 
subject  is.  This  Ave  do  by  acquiring  the  matter  of  its 
The  first  thing  class-conception.  I may  test  it  by  my  OAvn 
the  tociassqconii  senses — see  it,  touch  it,  taste  it,  smell  it, 
ception.  handle  it,  &c.,  in  which  case  I form  the  con- 
ception directly  from  the  object  itself.  This  Method  is 
By  observation,  called  Observation.  Or  I may  ask  some  one 

Maxims  ; Differentia  Maximarum.”  The  former,  as  the  word  denotes,  were 
Maxims ; that  is,  the  highest  generalization  of  truth  (Maxima  Genera) — 
to  be  used  as  Major  Premises  in  Processes  of  Deductions.  As  such,  they 
of  course  contained  the  Middle  Term,  and  furnished  thus  the  means  of 
proving  the  Copula  of  the  desired  Conclusion.  The  Differentia  Maximarum, 
consisted  of  one  or  more  words  expressive  of  the  point  in  which  one  Maxim 
differed  from  another. 


II.]  METHODS  OF  INVESTIGATION. SECT.  I.  221 

else  what  the  subject  is,  and  receive  from  him  either  its 
name  or  a description  of  it.  In  either  case  I form  the 
conception  from  the  observation  of  others — that  is,  from 
their  Testimony  • in  which  they  communicate  By  Testimony, 
to  me  what  they  have  observed.  This  is  the  Method  of 
Testimony ; and  the  only  difference  between  an  an- 
swer giving  a name  to  the  subject  and  a description  is, 
that  the  former  implies  what  is  expressly  stated  in  the 
latter. 

831.  At  the  first  observation  we  cannot  determine 
whether  the  observed  property  be  any  thing  DistiI?ction  of 
more  than  a separable  accident  or  not.  On  atrotheiese“onj 
a second  observation  of  the  same  individual,  observation- 
we  decide  at  once  that  all  of  the  properties  that  were 
different  in  the  two  observations  were  but  separable 
accidents  of  that  individual.  And  a third  and  fourth, 
as  well  as  each  successive  observation  may,  and  most 
likely  will  add  to  this  list  of  separable  accidents  some 
properties  that  had  not  been  so  regarded  before. 

835.  But  as  soon  as  our  observation  has  extended 
to  two  objects,  these  objects  are  referred  to  And a ciassifi- 
a class.  The  properties  which  they  have  in  cation  also- 
common  are  for  the  present  assumed  as  Formal,  consti- 
tutive of  the  class ; and  those  in  which  they  are  un- 
like, after  deducting  what  we  have  seen  to  be  separable 
accidents  in  each,  are  regarded  as  peculiarities  or  indi- 
vidual properties  of  each. 

836.  A wider  observation  embracing  more  indi- 
viduals always  brings  anew  classification.  A wider obser- 
Perhaps  the  bringing  in  of  a third  object  nfw0nci“smcaa 
may  give  us  two  classes — one  including  two  tion- 

of  the  three  objects,  while  the  other  will  be  so  unlike 
them  as  to  be  regarded  as  not  of  the  same  class  with 
the  other  two.  And  any  change  in  our  classification 
changes  our  view  of  the  properties  ; that  which  we  con- 
sidered an  individual  peculiarity  in  one  classification, 
becomes  a Formal  property  in  another  and  Material  in 
still  another. 

837.  In  the  process  of  classification  we  soon  come 


222 


LOGIC. — PART  II. 


[chap. 


to  find  that  one  property  which  we  had  made  Formal  of 
Recognition  of  one  class,  is  always  connected  with  another, 
as  Formal.  which  ot  course  therefore  may  be  predicated 
of  all  the  individuals  in  that  class  as  a mode  of  their 
existence.  We  see,  for  instance,  that  all  animals  that 
have  sharp  claws  are  predacious.  “ Sharp  claws  ” is 
a Formal  property,  and  “predacious”  is  a Modal, 
indicating;  their  mode  or  manner  of  life.  “ Unsup- 
ported bodies  fall  to  the  ground  ; ” — “ unsupported- 
ness ” is  the  Formal  property — “ falling  to  the  ground  ” 
is  the  Modal  property,  indicating  something  concerning 
their  mode  or  condition  of  being,  while  objects  belong- 
ing to  the  class  of  “ unsupported  bodies.” 

838.  But  “ unsupportedness  ” itself  may  be  and  in 
Accidental  pro-  fact  is  only  an  accidental  property.  The 
Formal.  same  object  may  be  “supported  at  one 
time  and  “ unsupported  ” at  another,  and  vice  versa. 
Hence  the  Modal  property  “ falling,”  will  be  acci- 
dental also. 

839.  But  we  soon  find  that  some  of  the  properties 
Recognition  of  which  are  not  in  the  class-conception,  and 
implied.  ot  course  therefore  were  not  known  to  us  at 
our  first  acquaintance  with  the  object,  are  not  only 
inseparable  from  the  object  so  far  as  we  have  seen  or 
known,  but  that  they  are  inseparable  from  it  abso- 
lutely. They  are  Implied  properties  necessarily  result- 
ing from  the  combination  of  the  properties  which  are 
included  in  the  class-conception,  as  the  laws  of  motion, 
for  instance,  in  the  conception  of  Matter  as  inert  [791]. 

840.  This  distinction,  however,  between  the  Modal 
Distinction  be  and  the  Implied  properties  cannot  be  shown 
Forma! m proper  a posteriori , or  by  any  of  the  Methods  of 

ties  not  shown  T ^ ^ 

a posteriori.  Investigation. 

811.  Methods  of  Observation  are  therefore,  and  of 
investigation  of  necessity  a posteriori,  with  regard  to  all  the 
implied  proper  Accidental  and  Modal  properties  of  oh- 
ori.  jects. 

842.  But  in  the  case  of  the  Implied  properties,  it  is 
for  the  most  part  in  actual  experience  no  less  so. 


n.]  methods'  of  investigation. — sect.  n.  223 

These  properties  are  not  included  obviously 
in  the  first  perception  of  an  individual  ob-  vestighed0  mi 
ject.  But  we  first  observe  the  property, 
or  something  which  suggests  it,  and  then  we  prove 
its  reality  a prior  i.  Thus,  suppose  I have  a And  proved  o 
circle  before  me,  I observe  its  radii ; I see  pTion- 
that  they  are  equal  to  each  other,  or  at  least  more 
nearly  so  than  any  difference  that  I can  measure  by 
my  eye.  I start  with  the  hypothesis  that  they  are 
equal,  and  measure  them  ; this  is  a posteriori  method 
of  proof.  It  can,  however,  never  approach  to  any  thing 
more  than  something  less  than  any  measurable  differ- 
ence between  the  radii.  But  by  a priori  demonstra- 
tion we  can  prove  that  they  are  equal  as  a fact,  because 
of  necessity  they  must  be  so. 

813.  So  too  with  the  Formal  property  of  any  spe- 
cies. The  web-feet  of  aquatic  birds,  for  instance.  We 
may  conjecture  from  the  examination  of  such  Modal  proper- 
feet  that  they  are  designed  for  swimming  ; conjecuSed  bl 
and  hence  indicative  of  the  Modal  property  pTtorL 
“ aquatic,”  as  applied  to  birds.  W e form  the  hypo- 
thesis [ Jingo  Tiypothesin\ , “ that  web-footed  birds  are 
aquatic.”  We  appeal  to  observation — fhat  is,  we  inves- 
tigate the  hypothesized  predicate  a posteriori,  and  find 
it  true. 

Sid.  Then  Analysis  of  the  class-conception,  further 
Inquiry  and  Observation,  Measurement,  Calculation  and 
the  various  other  Methods  of  Investigation,  will  give 
us  further  predicates  to  the  subject.  We  will  therefore 
proceed  to  treat  these  Methods  separately. 

SECTION  II. 

Of  Observation  and  Testimony . 

815.  Observation  is  the  first  and  most  primary  of 
all  the  Methods  of  Investigation.  From  the  moment 
that  we  open  our  eyes  upon  the  objects  of  this  world, 
we  begin  to  be  observers  of  what  is  taking  place  in  it. 


LOGIC. PAKT  n. 


224 


[chap. 


Each  of  our  Senses  is  an  avenue  through  which  infor- 
mation is  constantly  coming  in. 

846.  But  of  the  psychological  powers  and  of  the 
grounds  of  belief  in  what  we  tlms  observe,  it  is  not 
my  design  to  speak  here.  We  all  perceive  external 
objects,  we  form  conceptions  of  them  immediately,  we 
classify  them,  we  believe  in  their  reality,  and  never 
do  or  can  seriously  distrust  the  testimony  of  our 
senses. 

847.  Our  primary  Method  of  obtaining  a know- 
observaiion  the  ledge  of  the  facts  and  events  of  the  external 
thodary  c world,  and  of  the  properties  and  relations  of 
the  objects  existing  there,  is  Observation.  When  by 
our  own  agency  the  facts  which  we  wish  to  observe 
are  either  brought  into  existence  or  under  our  observa- 
Experiment.  tion,  the  Method  is  called  an  Experiment. 
Experiment,  therefore,  is  a Method  of  Investigation 
differing  from  Observation  only,  in  the  purely  acci- 
dental circumstances  of  the  observed  fact  having  been 
voluntarily  produced  by  ourselves  for  the  purpose  of 
the  Observation. 

848.  For  the  observation  of  the  facts  of  the  external, 
or  material  world  we  have  the  five  senses  : Sight , 

Means  of  ob-  Touch , Hearing , Smell , and  Taste.  For  the 
servation.  facts  of  the  interior  world,  those  which  pass 
within  the  Soul,  we  have  the  single  faculty  or  interior 
sense  called  Consciousness. 

849.  In  both  these  cases  the  same  faculty  gives  us 
subject  and  both  the  Subject  and  the  Predicate  included 

Predicate  seen  . ° . . -i  • 

as  one.  in  the  one  perception,  and  with  the  intumive 
judgment  affirming  the  one  of  the  other  as  property  of 
a Subject.  Thus,  1 see  a rose  and  that  it  is  red,  I smell 
that  it  is  fragrant,  I touch  that  it  is  soft  and  velvety. 
I am  conscious  of  thinking,  and  that  my  thought  is 
dull  or  active  ; I am  conscious  of  admiring,  and  that 
my  admiration  is  profound ; I am  conscious  of  envy, 
and  that  envy  makes  me  unhappy. 

850.  From  these  intuitive  perceptions  of  the  senses 
there  is  no  appeal,  or  if  there  is  there  is  no  means  of 


II.]  METHODS  OF  INVESTIGATION. SECT.  n.  225 

settling  that  appeal.  One  sense  may  indeed  sometimes 
correct  a judgment  based  upon  another.  No  appea 
Thus,  by  a touch  I may  find  that  what  I 
had  supposed  from  sight  alone  to  be  a peach,  ceptions- 
is  but  a piece  of  stone  so  carved  and  colored  as  to  look 
precisely  like  a peach.  But  in  this  case  it  is  only  one 
sense  acting  in  its  appropriate  sphere,  furnishing  means 
to  correct  the  too  hasty  judgment  based  upon  the  data  . 
furnished  by  another.  Nor  is  there  any  reason  to  trust 
one  sense  any  more  than  another,  when  each  are  exer- 
cised within  their  appropriate  spheres. 

851.  So  with  consciousness.  If  I am  conscious  of 
believing,  or  doubting,  or  remembering,  there  Noappeal  from 
can  be  no  appeal  from  my  consciousness.  consciousnesa- 
The  fact  may  be  miscalled.  Thus,  I may  call  the  feel- 
ing of  which  I am  conscious  humility,  when  all  others 
will  see  that  it  is  but  spiritual  pride.  The  mistake, 
however,  is  in  the  name  and  not  in  the  fact  that  I have 
some  feeling. 

852.  The  Predicates  of  any  Subject  may  express 
either  (1)  the  Implied  Properties  affirmed  in  Matter  ex- 
Synthetic  Judgments  a priori.  (2)  Modal  Predicates"  the 
Properties  exjiressing  the  Final  cause  of  any  Property 
included  in  a class-conception  considered  as  a Formal 
Property ; and  (3)  Accidental  Properties  denoting 
(a)  that  which  distinguishes  one  individual  from  an- 
other, or  (Jj)  that  which  distinguishes  an  individual 
from  itself  in  another  condition  or  at  another  time  ; 
(I)  (a)  the  Cause,  or  ( b ) Effect,  and  (5)  the  Quantity. 

853.  Now  as  all  investigation  begins  with  indi- 
vidual objects,  a property  when  first  brought  to  our 
minds  cannot  be  referred  to  any  of  these  classes  ; for 
at  first  we  do  not  know  that  it  is  any  thing  more  than 
a separable  accident,  nor  in  fact  do  we  know  that  it 
is  not. 

854.  In  the  course  of  our  investigations  we  may  oc- 
cupy either  of  two  different  positions  in  rela-  investigation 
tion  to  the  Subject.  We  may  be  investigat-  of  Authorities! 
ing  it  de  novo , or  we  may  be  merely  following  an  inves- 

10* 


226 


LOGIC. PAKT  II. 


[CHAP. 


tigation  made  by  some  one  else  before  us.  In  this 
latter  case  we  are  learning  from  Testimony  or  Au- 
thority, from  the  Force  of  Terms  or  from  the  Common 
Sentiment  of  mankind.  In  all  these  cases  we  are 
not  investigating  the  subject,  but  we  are  looking  for 
the  result  of  an  investigation  made  by  some  one 
else. 

855.  But  if  we  are  investigating  the  subject  itself, 
* and  looking  for  properties  and  relations  which  are  not 

obvious  on  the  first  sight,  it  will  be  found 

Use  of  Hypo-  . . , 1-.°  ’ , 

theses  in  Hues-  necessary  in  almost  all  cases  to  form  some 
hypothesis  or  conjecture  of  what  this  pro- 
perty is  to  be.  This  hypothesis  serves  something  the 
same  purpose  as  the  x , which  is  the  representative  of 
the  unknown  quantity  in  Algebraic  Equations.  Thus, 
suppose  one  is  trying  to  discover  the  Cause  of  any 
phenomenon  ; he  would  need  to  make  a supposition 
beforehand,  and  proceed  to  test  its  correctness  by  facts 
and  observations.  Few  discoveries  have  in  fact  ever 
been  made  except  under  the  guidance  of  a shrewd 
guess,  conjecture,  or  hypothesis  of  what  the  truth  or 
fact  is  to  be  when  it  is  found. 

Having  noticed  the  principal  Methods  by  which 
we  can  investigate  subjects  by  the  direct  application 
of  our  faculties  to  the  subjects  themselves,  let  us  con- 
sider Testimony,  or  the  Means  by  which  we  avail  our- 
selves of  the  exercise  of  the  faculties  of  others  upon  the 
subject  of  our  inquiries. 

856.  Of  these  we  have  two  distinct  classes  : (1)  Sub- 
jects which  we  might  investigate  directly  ourselves  if 

Kinds  ofTes-  we  had  fhe  opportunity  and  means ; and 
timony.  [2)  the  Predicates  which  depend  upon  Au- 
thority, or  the  expressed  Will  of  another. 

857.  For  by  far  the  largest  part  of  what  we  know, 
or  at  least  by  far  the  largest  part  of  the  facts  upon 
Testimony  as  a which  we  have  to  depend  in  forming  our 
™eeana  ofiserva6  opinions,  constructing  our  systems,  as  well 
lions  of  others.  as  for  the  practical  purposes  of  life,  we  are 
obliged  to  depend  upon  the  observations  of  others ; 


II.]  METHODS  OF  INVESTIGATION. SECT.  II.  227 

their  statements  of  what  has  come  within  their  expe- 
rience and  observation  is  called  Testimony. 

858.  The  use  of  Testimony  supposes  that  others 
have  the  same  faculties  and  means  of  know-  Th  use  0f 
ing  as  ourselves,  and  opportunities  which 

we  have  not  had.  This  fact,  however,  leads  nStchhad 
us  to  investigate  the  nature  and  value  of  ourselves- 
Testimony.  And  I shall  at  present  speak  of  Testimony 
only  by  itself,  referring  to  a subsequent  Chapter  in 
which  I shall  speak  of  the  Concurrence  of  Testimony, 
as  giving  demonstrative  force  to  simple  Testimony. 

The  value  of  Testimony  is  to  be  estimated  Tests  of  the 

t . -l  _/?  n • , , d value  of  Testi- 

by  the  following  tests  : mony. 

859.  (1)  The  nature  of  that  concerning  which  the 
testimony  is  given. 

Some  facts  are  obvious  in  themselves,  easily  seen, 
and  not  easily  misunderstood — snow  on  the  Nature  of  the 
face  of  the  earth,  a mountain,  a desert,  a subject  mat,er- 
loud  noise,  and  such  like  facts,  are  too  obvious  to 
diminish  aught  on  that  ground  from  the  value  of  testi- 
mony to  their  reality. 

860.  But  in  a large  variety  of  cases,  the  fact  is 
beyond  the  reach  of  human  faculties,  and  that  which 
is  reported  as  the  fact  is  merely  the  inference  Reporting theo- 
froin  the  fact.  Thus,  take  all  the  reported  nes  ii,r  fects- 
cases  of  demoniacal  possession,  witchcraft,  second-sight, 
&c.  The  fact  really  testified  to  is  beyond  the  reach 
of  the  senses — a mere  inference  from  what  was  seen. 
One  might  see  that  another  was  acting  strangely  and 
report  those  acts,  but  to  see  that  there  was  demoniacal 
possession,  the  presence  of  the  spirit  of  one  departed, 
or  any  of  that  kind,  is  of  course  quite  impossible.* 

861.  So  too  in  reporting  the  acts  of  another.  A 

* Of  course  I am  not  questioning  the  reality  of  such  facts,  and  espe- 
cially demoniacal  possessions  when  properly  vouched  for.  The  testimony  of 
our  Lord  in  the  Nerv  Testament  is  of  course  that  of  a competent  witness. 
But  for  all  persons  who  have  nothing  beyond  the  ordinary  insight  of  mor- 
tals, the  demoniacal  possession,  witchcraft,  &c.,  must  be  only  a theory  to 
explain  the  observed  facts. 


228 


LOGIC. PART  II. 


[chap. 


witness  might  speak  of  his  motives  as  facts  that  he  had 
Motives  tor  observed,  and  testify  that  such  a person  was 
the  acts.  angry,  or  jealous,  or  benevolent,  &c.,  when 
the  moral  states  could  he  nothing  more  than  inferences 
from  what  was  seen.  The  facts  which  could  be  seen 
and  testified  to,  and  the  inferences  from  those  facts, 
must  be  carefully  distinguished. 

862.  (2)  The  intelligence  of  the  witnesses.  In  many 
cases  this  is  of  slight  importance,  since  the  fact  may 
intelligence  of  he  s0  obvious  as  that  no  one  could  mistake, 
the  witness.  But  jn  others  it  is  far  otherwise.  The  testi- 
mony of  a physician,  for  instance,  to  a disease  with 
which  an  invalid  is  suffering,  would  be  of  vastly  greater 
value  than  that  of  one  who  knew  nothing  of  medicine, 
and  had  scarcely  ever  seen  a sick  person  in  his  life. 

863.  (3)  Opportunity  to  know  is  reckoned  as  one 

of  the  fundamental  points  in  the  value  of  testimony, 
opportunity  to  One  should  speak  of  what  he  has  heard  and 
know  seen.  If  he  only  reports  what  he  has  heard 

others  say  of  what  they  have  heard  or  seen,  the  testi- 
mony becomes  of  constantly  less  value  at  each  remove 
from  the  original  witness. 

864.  (4)  Integrity  or  moral  honesty  in  the  witness 
Moral  charac-  is  of  course  an  important  element  in  the 

ness"  16  vaiue  of  testimony.  Without  it  the  witness 
may  be  only  imposing  upon  us  the  fictions  of  his  own 
imagination  instead  of  any  outward  realities. 

865.  (5)  And  finally,  since  there  are  but  few  if  any 
persons  without  some  prejudices,  feelings  of  personal 
Freedom  from  interest  or  passion,  or  attachments  to  theory, 
prejudice.  which  will  very  much  influence  the  value 
of  testimony,  it  is  seldom  if  ever  safe  to  take  the  testi- 
mony of  any  one  without  knowing  something  of  his 
animus  in  regard  to  the  subject-matter,  and  guarding 
against  its  influence  upon  the  testimony  itself.  There 
is  scarcely  any  event  or  fact  that  has  not  two  sides  to 
it,  and  its  appearance  will  depend  very  much  upon  the 
side  which  is  presented  to  us,  or  from  which  we  choose 
to  view  it.  A traveller  with  aristocratic  notions, 


II.] 


METHODS  OF  INVESTIGATION. SECT.  II. 


229 


travelling  in  Europe,  and  constantly  received  into 
aristocratic  circles,  and  receiving  the  kindest  civilities 
from  that  class  of  the  population,  seeing  every  thing 
from  their  position  and  with  their  eyes,  would  report  a 
very  different  class  of  facts  from  one  who  should  walk 
on  foot,  associate  with  “ the  toiling  millions,”  and  see 
life  as  it  passes  with  them. 

866.  We  must  also  remember  that  testimony  to  be 
of  any  value  must  be  positive.  More  mis-  Testimopy  must 
chief  has  been  done  by  the  neglect  of  this  be  P0Sltive- 
fact,  obvious  as  its  importance  is,  than  one  would  at 
first  believe. 

A good  illustration  of  this  mistake  is  seen  in  the 
case  of  the  Irishman,  who  is  said  to  have  complained, 
because  he  was  convicted  on  the  testimony  of  one  wit- 
ness, who  saio  him  commit  the  offence , when  there  were 
hundreds  that  did  not  see  him  commit  it. 

867.  Omissions  of  this  kind  are  most  likely  to  occur 
in  the  midst  of  statements,  where  other  cir-  omissions 
cumstances  or  occurrences  are  mentioned.  to 
Thus  a very  common  case,  in  theological  cur- 
controversy,  is  in  the  testimony  of  an  ancient  Father, 
that  “ in  Alexandria,  from  the  days  of  St.  Mark,  the 

• Presbyters  were  accustomed  to  select  one  of  their 
number,  place  him  on  the  throne,  and  call  him  their 
Bishop.”  No  mention  is  here  made  of  his  having  been 
ordained,  as  a part  of  the  process  by  which  he  was 
placed  in  the  ofiice  of  Bishop,  and  hence  it  has  been 
argued  that  there  was  no  ordination. 

868.  The  mere  omission  to  mention  the  occurrence 
of  what  was  customary,  is  no  proof  that  it 

did  not  occur.  History,  from  the  necessities  testimony11  o° 
of  the  case,  is  full  of  such  omissions.  It  is  pr00t' 
impossible  to  state  all  that  occurred,  and  if  it  were 
stated  no  one  could  read  the  hooks  that  would  be 
written,  nor  could  the  world  contain  them. 

Hence  writers  do  not  usually  mention  that  most  likely  to 

i be  omitted. 

which  is  so  common  as  that  it  is  never 
omitted,  and  is  perfectly  well  understood  by  those  to 
whom  the  writings  are  addressed. 


230 


LOGIC. PAKT  II. 


[chap. 

869.  But  even  positive  testimony  to  a negative  pro- 

positive  Testi-  position  can  never  be  equal  to  positive  testi- 
“hve ‘propost  niony  to  an  affirmative  one.  Positive  testi- 
tlon-  mony  to  a negative  proposition,  like  negative 

testimony,  is  for  the  most  part  only  the  absence  of 
testimony. 

870.  Positive  testimony,  supposing  there  is  no 
fraud  or  mental  hallucination,  can  be  accounted  for 
only  on  the  ground  of  the  reality  of  that  which  was 
seen,  heard,  &c.  Testimony  to  a negative,  however,  may 

always  be  accounted  for  on  the  ground  of  in- 
litnony.how  ac-  ability  or  inattention  on  the  part  of  the  wit- 
Loumc  or.  nesSj  as  wep  as  py  the  absence  of  that  which 
he  did  not  perceive.  If,  however,  one  man  should 
testify  that  he  had  seen  an  extraordinary  phenomenon, 
and  a large  number  of  others — even  two  or  three  other 
persons,  having  their  attention  directed  to  the  same 
object  or  place,  and  occupying  a position  equally 
favorable  as  that  of  the  man  who  pretended  to  see  it— 
did  not  see  it,  this  conflict  of  testimony  would  always 
raise  the  question  of  the  sanity  of  the  mind  and  facul- 
ties of  the  affirming  witness,  over  and  above  the  ques- 
tion of  his  veracity.  In  all  such  cases  the  contradiction 
in  the  testimony  must  be  in  some  way  accounted  for 
before  either  can  be  received,  unless  it  be  in  cases 
where  one  side  is  vastly  preponderant  against  the 
other.  Such  a disparity  may  in  itself,  unless  it  can  be 
accounted  for  otherwise,  be  taken  as  a sufficient  gua- 
rantee of  the  accuracy  of  the  testimony  on  that  side. 
But  in  all  these  estimations,  ceteris  paribus , the  pre- 
ponderance is  always  on  the  side  of  the  affirmative 
testimony. 

871.  Again,  we  must  always  distinguish  very  care- 
Fact  ami  infer-  fully  between  what  is  seen  and  the  inference 
Fact. ,rum  the  from  it,  Perhaps  there  is  no  case  that  illus- 
trates this  so  well  as  the  common  belief  and  testimony 
to  the  fact  that  the  sun  rises  and  sets.  The  fact  is  a 
relative  change  in  position — the  motion  of  the  sun  is 
but  an  inference  or  a theory  to  account  for  that  fact. 


II.J 


METHODS  OF  INVESTIGATION. SECT.  II. 


231 


The  fact  we  take  as  indisputable,  the  theory  we  reject 
whenever  we  can  show  that  there  is  a better  one  or  that 
it  is  unnecessary. 

872.  The  truth  of  a priori  propositions  we  con- 
ceive to  be  independent  of  any  Will  or  of  any  Mind 
even.  They  are  necessary  truth,  and  therefore  abso- 
lutely true.  Their  truth  depends  upon  no  Testimony  not 
condition  whatever.  Hence,  in  JNecessary  sary  Matter. 
Matter  we  seldom  make  use  of  Testimony,  or  the 
authority  of  others. 

873.  But  with  regard  to  physical  truths,  although 
their  being  true  depends  upon  the  Will  of  In  Physical 
the  Creator  or  First  Cause  of  them,  yet  we  ^‘“ho 
know  the  Predicate  from  an  observation  of  only- 

the  Subject  itself.  We  have  but  to  look  at  a rose  to 
see  that  it  is  red,  to  taste  an  orange  to  see  that  it  is 
sweet,  &c.  From  this  observation  of  the  properties  in 
the  effect,  we  infer  the  intention  or  will  of  the  Intelli- 
gent Cause,  which  is  the  Creator.  In  Physical  Matter, 
therefore,  Testimony  can  be  properly  used  only  to 
facts.  It  can  never  establish  theories  or  opinions,  but 
only  facts  ; the  fact  that  this,  that,  and  the  other 
man  held  the  theory,  and  upon  what  grounds  he 
held  it. 

874.  But  in  Moral  Matter  we  can  never  learn  the 
properties  of  subjects  by  any  mere  investigation  of  the 
subject  itself.  They  depend  upon  the  will  Testimony  m 
of  him  from  Avhom  they  proceeded.  Of  ^thm- 
these  things,  therefore,  our  only  means  of  ity- 
knowledge  is  the  Testimony  of  some  one  who  knew  the 
will  and  intention  of  the  Authority  from  which  they 
emanated.  Thus,  in  Revelation  we  have  Sacrifice, 
Baptism,  the  Holy  Eucharist,  the  Lord’s  Day,  &c. 
Of  these  no  one  knows  or  can  know  what  is  to  be  pre- 
dicated of  them  in  certain  respects  except  from  Reve- 
lation itself.  And  Revelation  is  a Testimony  to  the 
Will  of  God  concerning  those  elements  of  Religion. 
Of  Baptism,  for  instance,  we  can  know  what  it  is  ; how, 
by  whom,  and  to  whom,  it  is  to  be  administered,  and 


232 


LOGIC. PART  II. 


[CHAP. 


what  is  its  efficacy  upon  the  worthy  recipient,  only 
from  the  Scriptures.  All  of  these  are  questions  that 
never  can  be  answered  by  any  study  of  the  subject, 
Baptism,  itself ; but  only  by  a study  of  the  Revelation, 
which  is  Testimony  to  the  Will  of  God  concerning  it. 

875.  So  it  is  in  every  society  and  organization  of 
positive  insti-  men.  There  are,  and  of  necessity  must  be, 
societies.  some  positive  rules  and  institutions  not 
dependent  upon  any  one’s  sense  of  propriety,  but 
ordained  by  the  consent  of  the  collective  whole  ; or  at 
least  by  the  authority  that  acts  for  that  whole.  And 
these  statutes,  constitutions,  canons,  by-laws,  &c.,  by 
whatever  name  they  are  called,  become  the  Testimony 
by  which  we  investigate  the  properties  which  may  be 
predicated  of  the  subjects  treated  of  in  those  docu- 
ments. 

876.  Again,  Lexicons,  Dictionaries,  and  such  like 
Dictionaries  compilations,  are  Testimonies  which  we  use 

»iee  meaning o?  as  a means  of  investigating  the  meanings 
words.  and  definitions  of  words.  Analysis  is  often 
of  great  service.  When  a word  is  compounded  of  two 
or  more,  or  is  used  in  a derivative  form,  we  can  often 
get  an  important  suggestion  towards  its  meaning  from 
an  analysis  of  the  word  into  its  parts — or  as  gramma- 
rians say,  from  its  Etymology.  Rut  the  real  force  and 
meaning  of  a word  after  all  will  depend  upon  the  usus 
loguendi ; and  a Dictionary  or  Vocabulary  is  but  a 
Testimony  to  that  usage  of  a language  which  deter- 
mines the  meaning  of  words. 

SECTION  III. 

Of  Measurement  and  Calculation. 

877.  Measurement  as  a Method  of  Investigation 
requires  a mention,  although  there  is  but  little  to  be 
said  of  it.  It  is  the  Method  by  which  we  find  the 
Predicates  that  answer  the  questions  “ how  many  ? ” 
“ how  much  ? ” “ the  time  when  % ” &c. 


II.]  METHODS  OF  INVESTIGATION. — SECT.  HI. 


233 


878.  We  may  have  a definite  answer,  or  only  an 
indefinite,  or  comparative  one.  Tims,  if  one  DL,finite 
ask  how  high  Mont  Blanc  is,  he  may  obtain  comparative 
the  indefinite  comparative  answer,  “It  is 

the  highest  of  the  Alps.”  Such  answers  give  of  course 
hut  indefinite  answers,  by  comparing  the  thing  which 
is  unknown  to  the  inquirer  with  something  which  is  or 
is  supposed  to  be  known  to  him. 

879.  But  for  a definite  answer  in  Quantity,  it  is 
always  necessary  to  assume  some  unity  or  Assumed  unit, 
standard,  and  to  give  the  answer  in  the  number  of 
the  units  of  the  assumed  standard,  comprehended  in 
the  object  to  be  measured.  Hence  we  have  our  tables 
of  unities  in  long  measure,  as  “ inches,”  “ feet,”  “ fur- 
longs,” “miles,”  “leagues.”  We  have  also  unities  of 
measure  in  time,  in  weight,  in  solid  quantity,  &c. 

880.  Some  such  Method  is,  I apprehend,  that  which 
in  fact  gives  us  the  first  hypothesis,  or  hypo-  Measurement 
thetical  knowledge  of  the  implied  properties  fearni,”ethesim- 
of  the  subjects  treated  of  in  the  sciences  of  Sfe6ePompewi!3 
Continuous  Quantity,  Geometry,  Trigono-  Fit'urea- 
metry,  &c.  Such  implied  properties  there  are  in  every 
class-conception.  They  are  likely  to  be  brought  to  our 
knowledge  first  by  some  one  of  the  Methods  of  Investi- 
gation (and  may  be  brought  tp  our  mind  by  any  of 
them).  But  when  they  are  so  brought  to  our  minds, 
they  must  be  proved  by  Demonstration,  which  we  have 
treated  as  one  of  the  Methods  of  Proof.  Thus,  I may 
learn  at  first  from  actual  measurement , that  the  square 
of  the  hypothenuse  of  a right-angled  triangle  is  equal  to 
the  sum  of  the  squares  of  the  two  other  sides,  and  then 
prove  it  as  a necessary  and  invariable  property  of  all 
right-angled  triangles  a priori.  Such,  I ’suppose,  has 
been  the  method  in  which  most  of  the  Predicates  that 
are  now  affirmed  a priori  were  first  discovered  ; they 
were  first  learned  a posteriori  by  observation  or  mea- 
surement, and  then  affirmed  on  a priori  grounds. 

881.  It  is  not,  however,  the  Method  of  their  Dis- 
covery but  their  Proof  which  determines  between  the 


LOGIC. — PART  II. 


234 


[chap. 


Synthetic  Judgments  a 'posteriori  and  those  which  are 
a priori. 

882.  AViien  the  question  relative  to  quantity  is, 
counting  a “ how  many  ? ” we  have  as  preparatory  to 

Method  of  In-  -i  , , • ■ ,,  II  J 

vestigation  in  calculation  “ counting , as  a means  of  enu- 
tity.  meratmg  the  number  ot  individuals  m any 

Logical  Whole.  In  this  case  the  unity  is  not  assumed 
but  is  given.  It  is  the  logical  individual. 

883.  Arithmetic,  Algebra,  and  the  Calculus  are 
Methods  of  but  Methods  of  Investigation  in  Discrete 

calculation.  Quantity.  They  presuppose  counting  or 
enumeration  by  individuals  as  units  of  number. 

884.  Of  course  we  cannot  go  into  a consideration 
of  these  Methods  in  detail  here.  To  do  so  would 
require  a Treatise  on  Arithmetic,  Algebra,  and  the 
Calculus.  I will  in  this  place  therefore  specify  only 
what  is  essential  to  all  of  them. 

885.  The  Methods  described  in  the  works  on  these 
Methods  in  subjects,  are  determined  rather  by  the  Idea 

determined'1  by  of  the  Useful  than  by  the  Idea  of  the 
usefuiea  °‘ the  True.  They  all  come  to  the  same  result, 
and  the  superiority  of  the  one  over  the  other  consists 
in  its  superior  usefulness  ; that  is,  it  is  a shorter  and 
more  useful  way  of  doing  what  may  be  done  in  some 
other  way. 

886.  So  far  as  the  Idea  of  the  True  determines 
them,  there  are  but  two  radically  distinct  Methods  of 

Logically  but  Calculation : (1)  when  the  parts  are  gi  ven 
two  Methods.  -gnq  the  whole  ; and  (2)  when  the  whole 
with  some  of  the  parts  are  given  to  find  the  other,  or 
others  if  there  be  more  than  one. 

887.  For  the  first  Method  or  Addition  it  is  neces- 
conditions  of  sary  that  all  the  parts  be  given : one  of  them 
thod.hrst  Me"  at  ieast  a Discrete  Quantity  ; and  the  others 
so  as  to  be  ascertainable  by  means  of  the  one  thus 

given  ; thus,  ~ + 4 = x. 


II.]  METHODS  OF  INVESTIGATION. SECT.  HI. 


235 


In  this  case  the  three  terms  - + - + 4 are  the 

2 3 

and  x represents  the  whole,  which  is  still  an  unknown 
quantity.  By  the  Method  of  Addition  we  find  that 
quantity  and  substitute  it  for  x,  and  say  x — 24,  or 
twenty-four  is  the  whole.* 

* As  illustrating  this  point  we  may  refer  to  the  old  Sophism  of  Achilles 
and  the  Tortoise. — “ They  start  at  the  same  time  from  points  one  mile 
apart,  the  Tortoise  being  ahead.  While  Achilles  is  running  that  mile  the 
Tortoise  will  have  run  one-tenth  of  a mile.  But  while  Achilles  is  running 
that  one-tenth  of  a mile  the  Tortoise  will  have  run  one-tenth  of  one-tenth, 
that  is,  one-hundredth  of  a mile,  and  so  on  ;■  therefore  Achilles  will  never 
overtake  the  Tortoise.” 

Leibnitz  first  proposed  as  a solution  of  this  sophism,  and  it  has  been 
repeated  by  Coleridge  and  De  Quincey,  that  it  implies  the  infinite  divisibility 
of  space,  without  taking  into  account  the  equally  infinite  divisibility  of  time 
also.  I am  not  authorized  to  say  that  this  solution  is  not  satisfactory,  I sup- 
pose, hut  I really  cannot  see  that  it  has  any  meaning  that  is  to  the  purpose. 
Whately  says  that  Aldrich  and  the  old  Logicians  answered  by  proving  that 
the  Conclusion  is  false.  But  as  he  justly  remarks  that  is  no  answer,  if  the 
Premises  are  admitted  and  the  Formula  is  unquestionable.  Whately  an- 
swers by  saying  that  the  Argument  cannot  be  stated  Logically  at  all ; that 
is,  in  any  Logical  Formula.  But  to  this  we  reply,  so  much  the  worse  for 
the  Formulae.  If  there  is,  as  he  admits,  “ a seeming  demonstration,”  there 
must  be  a Formula  to  which  it  can  be  reduced,  though  it  may  be  of  course 
an  invalid  Formula.  Otherwise  it  must  be  reducible  to  a Formula  valid 
in  itself,  without  fulfilling  the  conditions  of  that  Formula. 

The  Sophism  can  be  reduced  to  a Categorical  Formula  as  well  as  any 
other  Algebraic  Equation.  The  expression  in  these  Formula  is  awkward 
and  unnecessary.  Mathematics  is  the  Logic  of  Continuous  and  Discrete 
Quantity.  Nor  is  there  the  slightest  necessity  of  bringing  their  arguments 
within  the  Formula  of  Logical  Quantity.  But  if  one  will  insist  upon  such 
a statement  of  the  Sophism  before  us,  it  will  then  he  found  that  the  word 
“ while  ” is  used  in  each  successive  Premise  in  different  senses.  Hence 
the  Fallacy  of  Ambiguous  Middle. 

Thus, — The  first  period  is  “ while  ; ” 

“ While  ” is  the  second  period  : 

.’.  The  first  period  is  [equal  to]  the  second. 

That  is,  it  takes  as  long  to  run  the  mile  and  the  tenth,  as  it  does  the  tenth 
and  the  hundredth — and  if  so  Achilles  will  never  overtake  the  Tortoise. 

But  in  the  Methods  of  Discrete  Quantity  the  fallacy  is  in  requiring  a 
Whole  without  giving  any  measure  of  the  parts.  The  Whole  is  “ the 
quantity  of  time  from  the  moment  of  their  starting  until  that  of  their  over- 
taking.” Now  undoubtedly  the  time  of  Achilles  running  the  mile  is  one 
part  of  that  Whole.  But  its  value  is  not  given  either  relatively  to  the  Whole 
nor  in  Simple  Quantity.  So,  too,  the  time  of  running  the  tenth  and  the 
one-hundredth  is  a part  of  the  Whole ; but  we  are  not  told  what  part,  nor 
how  long  it  is  in  Simple  Quantity. 


236 


LOGIC. — PART  II. 


[CHAP. 


8S0.  If  there  are  two  unknown  quantities,  the  Me- 
thod of  Adding  is  different ; hut  the  Method  of  Inves- 
tigating the  Discrete  Quantity  of  the  Whole,  or  finding 
the  Predicate  is  the  same,  namely,  it  is  Addition  of 
the  Parts. 

S89.  Or  again,  if  we  have  a Whole  and  some  of  its 
second  Method.  Parts  given,  to  find  the  other  part,  we  hav.e 
the  Method  of  Subtraction.  Thus, 

6 — 3 — 2 = x. 

Here  6 is  a Whole,  and  3 and  2 are  parts  of  the 
Whole,  and  x represents  the  other  unknown  part  which 
is  to  be  found.  By  Subtraction  we  find  it  and  say, 

x — 1. 

890.  But  Multiplication,  Division,  Involution,  Evo- 
Muitipiication,  lotion,  &c.,  &c.,  are  only  more  usef  ul  be- 
Divisfon, &c.  cause  shorter  Methods  to  the  same  results; 
that  is,  to  find  a whole  from  the  given  parts,  or  a part 
from  a whole — the  rest  of  the  parts  also  being  given  in 
Discrete  Quantity. 

891.  When  I speak  of  the  parts  and  the  whole,  &c., 

being  given,  I mean  that  they  are  virtually  given.  As 
The  parts  how  in  the  first  example  above  one  part  alone  was 
given.  given  in  pure  quantity,  4 ; but  it  was  given 

in  such  a way  that  the  value  of  the  others  could  be 
obtained  from  it.  It  was  given,  and  its  fractional  value 
in  relation  to  the  whole  was  also  given.  And  this  will 
always  be  found  to  be  necessary.  If  the  parts  are  not 
given  in  simple  quantity  they  must  be  in  or  reducible 
to  some  fraction  or  multiple  of  the  whole. 

892.  The  whole  must  of  course  also  be  homogeneous, 
parts  must  be  Thus,  if  we  add  6 and  8,  the  whole,  as  all 
homogeneous,  ^vlioles  in  pure  quantity  are,  is  homogeneous.. 

Now  from  such  a statement  we  can  simply  have  no  answer,  because 
the  Premises  are  inadequate.  But  the  Sophism  instead  of  saying  as  it 
should,  that  there  is  no  answer,  gives  a negative  answer,  which  is  of  course 
a very  different  thing. 

But  let  us  give  a value  to  either  of  these  parts  and  the  answer  is  easily 
obtained.  Suppose  that  Achilles  runs  at  the  rate  of  twelve  miles  an  hour, 
and  an  acquaintance  with  the  first  principles  of  Algebra  is  all  that  is 
required  to  find  the  answer. 


n.]  METHODS  OF  INVESTIGATION. SECT.  IV.  237 

It  is  merely  14 — not  fourteen  men  or  fourteen  dollars , 
or  any  thing  of  the  kind,  but  fourteen  simply. 

893.  But  if  we  have  six  men  and  eight  dollars , we 
cannot  add  them  into  a whole,  which  will  be 
expressed  by  any  name  m the  English  lan-  produce  a high- 

r c J J 1 9 er  Whole. 

guage.  buppose,  however,  we  have  six 

horses,  eight  cows,  twelve  sheep,  we  may  add  them, 
and  then  the  homogeneous  whole  is  not  horses,  cows, 
or  sheep,  but  it  may  be  denoted  by  a generic  term 
including  these  parts  as  species.  Such  a term  is  the 
English  word,  “ cattle  ” or  “ stock.” 

894.  And  for  the  same  reason  in  Division  the  divisor, 
and  in  Multiplication  the  multiplier,  must  be  Dlvisor  and 
pure  number;  while  the  dividend  and  the  beulpuie r num- 
multiplicand  may  denote  any  objects  in  Lo-  ber- 

gical  Quantity.* 


SECTION  IV. 

Of  Average  and  Exclusion. 

895.  It  is  sometimes  the  case  that  we  cannot  obtain 
an  exact  observation  of  a fact  which  we  wish  The  use  of 
to  use  in  our  calculations.  And  again,  there  Average- 
are  many  facts  differing  from  each  other  in  many 
points,  that  are  either  based  upon  and  indicative  of 
a law,  or  at  least  afford  results  of  great  importance, 
which,  however,  none  of  our  inductive  processes  can 
reach.  Such  facts  and  results  are  obtained  by  what  is 
called  the  Process  of  Average. 

896.  Average  is  obtained  by  adding  together  seve- 
ral results,  and  dividing  the  amount  by  the  How  obtain. 
number  of  results — these  results  must  of  ed- 
course,  therefore,  be  stated  in  Discrete  Quantity. 

* The  Method  of  investigating  or  calculating  Probabilities  has  neces- 
sarily been  anticipated  in  the  preceding  Part,  p.  87  et  seq.,  157  et  seq.  The 
justification  for  such  an  anticipation  is  in  the  fact  that  the  amount  of  pro- 
bability is  in  these  cases  an  essential  part  of  the  Copula,  and  therefore  im- 
plied in  the  formation  of  the  Judgment,  as  much  so  as  the  inclusion  of  the 
Subject  in  the  sphere  of  the  Predicate  in  Pure  Categoricals,  the  Sequence 
in  Conditionals,  or  the  Excluded  Middle  in  Disjunctives. 


238 


LOGIC. — PART  II. 


[chap. 


897.  For  example,  the  mariner  at  sea  is  desirous 
of  getting  the  precise  position  of  a heavenly  body. 

observations  But  from  the  rocking  of  his  vessel  it  is  im- 
at  sea.  possible  to  get  two  observations  precisely 
alike.  Let  him  take  several  and  take  the  average. 

898.  Again,  suppose  we  wish  to  ascertain  the  pres- 
sure or  weight  of  the  atmosphere.  We  find  that  the 

in  the  use  of  Barometer  does  not  indicate  exactly  the  same 
the  Barometer.  j)ressurc  twice  perhaps  in  a whole  month. 
Heat,  the  time  of  the  day,  the  currents  of  the  atmo- 
sphere, all  affect  it.  But  let  there  be  made  observa- 
tions several  times  a day  for  a year,  for  instance,  add 
them  all  together,  and  divide  by  the  whole  number, 
and  we  have  an  average  approaching  the  truth,  just  in 
proportion  to  the  extent  of  the  observations. 

899.  This  Method  is  of  vast  importance  in  the  col- 
lection of  Statistics,  and  has  given  us  some  of  our  most 

in  collecting  useful  facts  and  estimates  in  Political  Eco- 
statistics.  nomy,  in  the  doctrines  of  Insurance,  and  in 
fact  in  every  department  of  business  and  of  legis- 
lation. 

900.  Thus  it  is  found  by  Statistics  that  out  of  every 
one  hundred  thousand  infants  born  in  England  and 

statistics  of  Wales,  fifteen  thousand  die  the  first  year, 
Deaths.  five  thousand  more  in  the  second,  about  one 
in  four  of  the  whole  number  before  they  would  have 
reached  their  sixth  year,  and  scarcely  one-half  reach 
the  age  of  forty  years.  How  suppose  results  similarly 
obtained  from  other  places,  other  races  of  people,  other 
modes  of  treating  their  infants,  to  differ  in  the  propor- 
tion of  deaths  from  those  in  England  and  Wales,  we 
should  have  this  difference  as  a fact  to  be  accounted 
for,  and  its  investigation  could  scarcely  fail  to  lead  to 
knowledge  of  the  greatest  importance. 

901.  In  the  same  way  Physiologists,  by  dividing 
vitabiiity.  the  whole  number  of  population  between 
certain  periods,  of  five  years  say,  as  from  twenty  to 
twenty-five,  from  twenty-five  to  thirty,  and  so  on  by 
the  number  of  deaths  of  persons  of  that  age,  obtain  a 


n.J  METHODS  OF  INVESTIGATION. SECT.  IV.  239 

number  which  will  of  course  vary  with  the  proportion 
of  deaths  to  the  whole  population.  This  is  assumed  to 
represent  what  is  called  the  vitability  * of  men  and 
women,  during  these  different  periods  of  their  life.  In 
some  of  these  periods  the  vitability  of  the  males  is  greater 
than  that  of  the  females,  as  from  fifteen  to  twenty,  and 
from  forty  to  forty-five.  In  others  that  of  the  males  is 
greater  than  the  females.  In  this  way  definite  results 
are  obtained,  Avhich  are  of  the  greatest  value  in  the 
investigations  of  many  of  our  most  useful  as  well  as 
interesting  sciences. 

902.  Even  those  matters  which  are  supposed  to 
depend  chiefly  upon  the  will,  such  as  mar-  Inmoraimat- 
riage,  and  suicide,  are  found  to  yield  results  ter3- 
astonishing  from  their  uniformity.  Quetelet,f  the  Bel- 
gian statistician,  affirms  that  the  Belgian  people  pays 
its  annual  tribute  of  marriage  with  more  regularity 
than  that  of  death,  blot  only  does  the  total  Marriages, 
number  of  marriages,  as  well  in  towns  as  in  the  coun- 
try, follow  a constant  mathematical  law,  but  the  same 
regularity  is  observed  in  the  numbers  which  indicate 
the  marriages  between  bachelors  and  maids,  bachelors 
and  widows,  widowers  and  maids,  and  widowers  and 
widows.  So  in  respect  to  the  ages  at  which  marriage 
is  contracted,  there  is  an  astonishing  uniformity  in  the 
annual  returns.  In  regard  to  suicides  the  statistics  of 
France;};  for  a period  of  twelve  years  exhibit  suicides, 
a similar  uniformity.  Their  number  varies  but  little 
from  year  to  year.  It  is  less  in  December  than  in 
any  other  month.  From  December  it  increases  to 
June,  when  it  attains  its  maximum  and  then  diminishes 
regularly  until  December  again. 

903.  These  facts,  which  can  be  obtained  in  a form 
to  be  of  use  by  the  Method  of  Average 

only,  doubtless  imply  some  causes  extrinsic  extrinsic  to  the 
to  the  will  of  man,  and  which  therefore  are 

* Carpenter’s  Human  Physiology.  f Du  Systcmo  Social,  p.  67, 

\ Annuaire  de  l’Economic  Politique,  1851,  p.  200. 


240 


LOGIC. — PART  II. 


[chap. 

within  the  legitimate  sphere  of  scientific  investigation. 
They  furnish  a case  for  the  Methods  of  Elimination 
(Section  VII.  below). 

904.  Now  where  there  is  uniformity  in  results, 
there  must  be  of  course  a cause  acting  under  a law  or 

uniformity  in  from  some  settled  design.  And  in  the  case 
this  law.  0f  intelligent  causes,  the  design  itself  gives 
the  law  to  its  activity  and  determines  it.  But  in  Na- 
ture, where  the  Causes  are  considered  as  mere  Forces, 
acting  without  intelligence  of  their  end  or  of  their  law, 
uniformity  is  always  considered  primarily  and  espe- 
cially as  implying  law — an  unchanging  rule  guiding 
the  activity  of  the  Force. 

905.  In  this  view,  the  Average  of  a single  series  of 
figures  might  indeed  be  valuable  in  many  cases,  as 

comparison  or  those  for  instance  specified  in  889  and  890. 
Averages.  But  stiH  its  great  value  as  a Method  can  be 
seen  only  in  its  application  for  the  purpose  of  com- 
paring the  average  results  of  different  series  of  figures 
relating  to  the  same  matter,  at  different  times  or  under 
different  circumstances,  as  in  the  cases  specified 
above  (894). 

906.  The  Method  of  Exclusion  is  used  for  abridging 
processes  of  investigation  by  the  exclusion  of  whole 
Method  of  ex-  classes  of  objects  as  individuals  from  the 
elusion.  necessity  of  examining  each  one  separately. 
The  exclusion  is  effected  by  means  of  properties  assumed 
as  differentia  of  species,  and  may  be  of  two  kinds. 

(1.)  The  exclusion  of  one  fact  or  species  of  facts 
First  variety.  after  another  from  any  given  Predicate 
assumed  as  the  Differentia  of  a species,  in  order  to 
include  a remaining  fact  or  class  of  facts  in  the  sphere 
of  that  Predicate. 

(2.)  The  exclusion  of  one  fact  or  subspecies  of  facts 
second  variety,  belonging  to  any  Proximate  Genus  from  one 
after  another  of  the  coordinate  species  in  that  genus, 
in  order  to  include  it  by  this  means  in  some  one 
remaining  species. 

907.  The  first  makes  or  implies  a statement  in  the 


n.]  METHODS  OF  INVESTIGATION. SECT.  IV.  241 

form  of  a Disjunctive  Judgment  with  the  Based,  upon 
Predicate  common  and  the  Subjects  coordi-  judgmSentnw‘ith 
nate,  as  either  A or  some  non-A  is  B [110].  fe°cts!inate  sub" 

908.  The  second  of  these  varieties  makes  or  implies 
a statement  in  the  form  of  a Disjunctive  Disjunctive 
Judgment  with  the  Subject  common  and  the  cpofdinStePre! 
Predicates  coordinate,  as  A is  either  B or  C,  dicates- 

or  D,  &c.  [408]. 

909.  This  Method  has  been  called  the  Abscissio 
Infiniti,  and  is  of  great  use  both  in  investi- 

gation  and  in  proof  It  partakes  m tact  so  su>  injinm,  its 
fully  of  the  Differentia  of  both  classes  of  Me-  Use' 
thods  that  we  are  in  doubt  with  which  of  them  to  place 
it  in  our  present  Treatise.  We  put  it  here,  however, 
because  we  are  treating  of  Methods  of  Investigation 
before  Methods  of  Proof. 

910.  Perhaps  the  best  illustration  of  the  first  form 
of  Abscissio  for  our  present  purpose,  is  the  niustration  of 
one  which  we  have  already  made  use  of  in  the  fim  variety, 
examining  the  validity  of  Moods  and  Figures  of  Syllo- 
gisms [478  et  seq.~\.  Thus  we  said  (or  rather  used  the 
implied  Disjunctive),  “ Either  those  with  negative 
Premises,  or  some  of  those  that  have  not  both  Pre- 
mises negative,  are  valid,”  we  completed  by  the  modus 
tollente  joonens  / proving  that  those  with  negative  Pre- 
mise could  not  be  valid.  "VVe  then  divided  the  re- 
maining coordinate,  “ those  which  have  at  least  one 
Premise  affirmative,”  into  two  coordinate  parts,  and 
said  or  implied  again,  “ Either  those  with  Particular 
Premises,”  or  “ some  of  those  whose  Premises  are  not 
both  Particular  are  valid ; ” and  proceeded  as  before 
until  we  come  to  the  species  of  which  alone  “ validity” 
could  be  predicated. 

911.  In  this  case  we  knew  at  the  outset  that  some 
of  the  individuals  included  in  the  divided 

whole — that  is,  some  syllogisms,  were  valid,  may  be  used 
But  if  we  had  not  known  this  we  could  even  bi-jl MA 1 
then  have  proceeded  in  the  same  method  not'J 
until  we  had  found  that  there  was  no  individual  in  the 

11 


24:2 


LOGIC. — PART  n. 


[chap. 


divided  whole  of  which  “valid”  could  he  predicated. 
In  that  case  we  should  have  ascertained  that  “ valid  ” is 
a Differentia  incompatible  with  the  Essentia,  which  is 
constitutive  of  the  Logical  Whole  as  a genus  ; that  is, 
with  the  Material  Properties  of  the  Logical  Moods. 

912.  But  in  this  case  there  would  have  been  only 
the  form  without  the  reality  of  a Disjunctive  Judg- 
ment. The  Disjunctive  would  have  been  merely  sup- 
posititious, designed  or  supposed  foT  the  sake  of  the 
Method,  since  a true  and  valid  Disjunctive  always  im- 
plies that  one  member  at  least  shall  be  true. 

913.  This  Method  is  often  of  great  use  as  a Method 
of  Proof  in  Geometry.  Thus  in  the  Theorem,  “ A line 

used  in  Geo-  let  fall  from  any  point  perpendicular  to  a 
metry-  straight  line,  is  the  shortest  distance  between 
the  point  and  the  line.  For  either  the  perpendicular 
is  the  shortest  line  or  some  not  perpendicular'  is  the 
shortest.”  But  as  the  perpendicular  makes  a right 
angle  with  the  line,  any  other  line  would  be  the 
hypothenuse  of  a right-angled  triangle,  of  which  the 
perpendicular  is  one  of  the  legs.  ILence  no  non- 
perpendicular line  is  the  shortest.  Consequently  the 
perpendicular  is  the  shortest.  This  Method  is  of  course 
vastly  shorter  than  that  by  which  we  prove  of  each 
possible  line,  not  a perpendicular,  separately — that  it 
is  not  the  shortest. 

911.  But  let  us  now  take  a case  of  the  other  kind, 
illustration  of  in  which  we  have  an  individual  or  several 
riety.  forming  a sub-species,  anu  are  desirous  ot 

finding  to  which  of  the  species  it  belongs — in  short  to 
find  what  it  is. 

915.  Let  us  take  for  an  illustration  a case  of 
chemical  analysis.  We  there  say  this  is  either  an 
acid  or  an  alkali.  We  test  it  and  find,  let  ns  sup- 
pose, that  it  is  not  an  acid.  It  is  therefore  an  alkali. 
We  must  say  this  is  either  potassa,  or  soda,  or  am- 
monia, &c.,  enumerating  all  of  the  alkalis.  We  pro- 
ceed as  before  and  test  it  for  potassa,  for  soda,  &c., 
until  by  proving  that  it  is  not  one  or  the  other  in  turn, 


n.] 


METHODS  OF  INVESTIGATION. — SECT.  V. 


243 


we  come  to  the  last.  But  of  course  it  is  quite  possible 
that  we  shall  find  which  species  of  alkali  it  belongs  to, 
that  is,  what  kind  of  an  alkali  it  is,  before  we  have 
tested  it  for  all.  Or  again,  as  in  the  former  case,  we  may 
test  a metal,  for  instance,  for  each  of  the  alkalis  in  turn, 
and  disprove  each  member  of  the  supposed  disjunctive 
in  turn,  and  thus  find  that  it  is  not  an  alkali  at  all. 
Here,  as  before,  the  Disjunctive  form  was  merely  sup- 
posititious— made#for  the  occasion,  without  knowing 
before-hand  that  the  individual  was  included  in  the 
Logical  Whole  at  all. 

SECTION  V. 

Of  Analysis. 

916.  We  may  have  two  kinds  of  Analysis  : (1)  An- 
alysis of  the  Conception,  and  (2)  Analysis  of 

the  Object  of  that  Conception.  The  former  conceptions  & 
is  Logical  Analysis  and  the  latter  is  Phy-  01  Subject°’ 
sical  Analysis. 

917.  We  have  seen  that  every  conception  of  a 
reality  contains  as  its  matter  certain  proper-  The  Matter  of 
ties  of  that  reality.  These  properties  make  ConcePtions- 
up  its  Essentia  and  Differentia  ; its  Essentia  as  includ- 
ing it  in  the  nest  superior  Natural  Genus  (thus  show- 
ing what  it  is) ; and  its  Differentia  limiting  or  deter- 
mining its  reality  by  showing  what  it  is>  not ; — thus 
giving  the  boundaries  that  separate  it  from  other 
objects. 

918.  The  Analysis  of  this  Conception  therefore 
gives  us  each  of  these  properties  as  separate  The  Analysis 
predicates,  which  may  be  affirmed  of  the  |ivS05fpVe0dr 
conception  of  the  object  as  a Logical  Sub-  jeadeof thecon- 
ject,  and  consequently  of  the  object  itself,  ception- 

if  the  conception  justly  and  properly  represents  it. 
Thus  we  may  say  of  a triangle,  “ it  has  three  sides  ; ” 
since  three-sidedness  is  necessarily  included  in  the 
conception  of  a triangle. 


244 


LOGIC. — PAKT  II. 


[chap. 


919.  So  too  in  Contingent  Matter.  The  Matter  of 
any  superior  and  comprehending  genus  is  always  con- 

Anaiysis  of  tained  in  the  conception  of  a lower  and 
contms'ntMat'  comprehended  species,  and  it  may  therefore 
ter-  be  evolved  as  a predicate  to  that  conception 

by  Analysis.  Thus  I may  say  of  a tree,  “ it  is  a vege- 
table ; ” of  an  ox,  u it  is  an  animal,”  &c.,  since  “ tree  ” 
and  “ ox  ” are  but  species  of  the  proximate  genera 
“ vegetable  ” and  “ animal.”  Or  we  may  predicate 
any  one  of  the  essential  properties  of  the  higher  genus, 
as  of  animal,  the  circulation  of  the  blood — of  the  tree, 
its  growth  from  a seed,  &c. 

920.  So  far  as  Predication  on  the  ground  of  Ana- 
lysis is  concerned,  it  is  of  but  little  if  any  consequence 
how  the  conception  which  we  analyze  was  formed. 

It  may  have  been  that  which  we  formed  in- 
conception  may  stmctively  on  our  first  comparison  ot  one 
of thehmicep-  object  with  another,  or  it  may  have  been 

that  more  elaborate  and  scientific  class-con- 
ception formed  by  scientific  investigation.  In  either 
case  we  may  analyze  the  concejition,  consider  the  ele- 
ments of  which  it  is  constituted  separately,  and  sepa- 
rately they  are  Predicates  which  we  may  affirm  of 
either  the  ciass-conception  or  of  any  individual  com- 
prehended under  it. 

921.  The  only  possibility  of  mistake  is  in  the  forma- 
tion of  the  conception  itself.  If  the  judgment  is  untrue 

the  conception  was  ill-formed.  Thus,  if  I 
ject o? thehon"  should  say  that  “ horses  have  wings,”  the 
cooceptimi  "lie  iude;ment  would  show  that  my  conception 

adequate.  n f?  l • i , J 1 

ot  “ horse  was  inadequate  or  erroneous. 
Or  in  popular  language,  one  would  say  that  I did  not 
know  what  I was  talking  about. 

922.  But  in  Geometry,  the  Mathematics  of  Con- 
tinuous Quantity,*  we  speak  only  of  the  conception  ; 

* In  Mathematics  we  deal  with  the  conception  exclusively.  The  very 
names  which  we  use  denote  the  conceptions  and  not  the  diagrams.  But  in 
what  is  called  contingent  matter  it  is  not  so.  The  names  denote  the  indi- 
viduals as  they  are  in  the  reality  of  being  or  existence.  With  these  the 


II.] 


METHODS  OF  INVESTIGATION. SECT.  V. 


245 


and  that  conception  is  one  which  we  have  formed  in  our 
own  minds  a priori,  and  by  a conscious  pro-  In  Mathematics 
cess  of  construction.  Hence  in  our  analysis  ™ 'TmSeous 
of  such  conceptions  we  merely  evolve  what  con^1'0113- 
we  had  consciously  and  designedly  put  into  it,  and 
there  is  no  liability  to  error.  Conceptions  cannot  be 
communicated  from  one  mind  to  another.  Each  mind 
must  form  them  for  itself,*  and  as  the  process  of  form- 
ing the  conception  of  a triangle,  for  instance,  is  the 
same  in  all  minds,  the  conception  itself  of  all  geometri- 
cal figures  must  be  the  same  in  all  minds. 

923.  But  in  forming  class-conceptions  of  the  objects 
in  the  external  world,  different  properties  of  the  objects 
themselves  will  seem  most  conspicuous  and 
characteristic  to  different  minds.  Hence  the  error  in  Con-  * 
matters  of  those  class-conceptions  will  be  dif-  u“°ent  MaMer' 
ferent  to  some  extent,  and  may  be  different  for  each 
mind.  Or  if  we  undertake  to  reconstruct  in  our  own 
minds  the  conceptions  which  others  have  formed  from 
their  description  of  the  objects  comprehended  under 
that  conception,  the  description  never  is  and  never  can 
be  quite  adequate.  Hor  will  it  be  understood  by  all 
minds  alike.  Every  one  has  a conception  of  “ apple,” 
for  instance,  and  yet  who  has  analyzed  that  conception 
so  that  he  can  enumerate  and  describe  precisely  every 
element  of  its  matter?  We  can  all  tell  an  apple  from 

a pear,  but  who  can  describe  precisely  and  exactly  all 
the  points  of  difference  between  them  ? Some  of  the 
most  striking  points  all  persons  can  give  ; but  no  one, 

I apprehend,  can  give  them  all. 

924.  The  question  will  always  arise,  therefore,  whe- 
ther the  elements  of  our  analysis  he  predicable  of  the 
individuals  comprehended  under  our  class-conception  ; 

thoughts  are  occupied,  and  while  in  the  former  case  we  ignore  the  differ- 
entia between  the  diagram  and  the  conception — in  the  latter  the  mind  is 
chiefly  occupied  at  first  with  those  Formal  Properties,  and  it  is  only  hy  a 
slow  process,  and  one  that  is  at  best  liable  to  error  and  mistake,  that  we 
arrive  at  the  class-conception  as  it  actually  existed  in  the  Divine  Mind. 

* See  Part  II.  Chap.  IV.  Sec.  I. 


246 


LOGIC. — PART  II. 


[CHAP. 


not,  however,  in  consequence  of  any  fault  or  fallacy  in 

False  conce  ^ie  analysis>  but  on  account  of  the  doubt 
tions"c  source  or  uncertainty  about  the  formation  of  the 
raise  state-  conception  itseit.  And  many  persons  are 
charged  with  intentional  falsehood  when  the 
fault  is  not  the  moral  one  of  uttering  what  they  know 
to  be  false.  It  is  merely  the  misfortune  of  having  so 
conceived  the  subject  as  that  predicates  which  do  not 
belong  to  it  are  included  in  their  conception  of  it. 

925.  This  analysis  of  our  conceptions  is  carried  on 
Reason  the  by  the  Reason  itself ; and  the  Reason  pos- 

lysis.  sesses  a faculty  ot  insight  or  immediate  in- 

tuition for  the  facts  of  consciousness,  precisely  as  the 
external  senses  do  for  the  facts  of  the  external  world. 
Thus,  if  I see  that  my  class-conception  of  horse  includes 
the  property  of  solid-ungularity  [having  but  one  hoof 
for  each  foot],  I can  no  more  doubt  that  my 
mate  judge  of  conception  oi  horse  includes  that  property, 
us  correctness.  j.pan  j can  f-}up  the  horse  before  me  has  but 

one  hoof  for  each  foot  when  my  eye  is  distinctly  fixed 
upon  the  object  itself. 

926.  But  let  us  pass  to  the  consideration  of  the  ana- 
lysis of  the  object  itself.  We  cannot  here  give  any  pre- 
Anaiysis  of  the  cepts  or  rules  for  accomplishing  such  analysis, 
object  itself.  Those  rules  are  not  and  cannot  be  reduced  to 
any  simple  system.  Success  depends  to  a great  extent 
upon  original  gift.  It  is  a matter  of  quickness  of  in- 
sight in  the  Reason,  just  as  the  perception  of  colors 
and  of  sounds  is  matter  of  difference  in  the  constitu- 
tional peculiarities  of  the  eye  and  the  ear.  No  rules 
Can  be  given  which  will  enable  one  to  distinguish 
between  the  different  shades  of  color,  or  the  different 
tones  of  the  diatonic  scale  in  music.  If  one  cannot 
make  the  discrimination  without  rules,  no  rules  will 
enable  him  to  make  it. 

927.  In  chemistry,  however,  analysis  forms  so  large 

Rules  and  Me-  and  so  indispensable  a part  of  its  Methods, 
Natural  *n  scf-  that  the  rules  and  tests  for  analysis  have 
ences.  been  extensively  systematized  and  recorded. 


n.]  METHODS  OF  INVESTIGATION. — SECT.  V.  247 

Nearly  every  science  has  done  something  of  the  kind. 
But  the  most  that  can  he  reduced  to  rule  and  formula, 
will  in  all  cases  be  but  a comparatively  small  part  of 
what  is  to  he  done. 

928.  An  analysis  of  this  kind  is  always  an  experi- 
ment, and  the  elements  evolved  are  objects  AnaIysig  an 
of  observation  ; and  Ave  can  of  course  predi-  expenment. 
cate  them  of  the  object  analyzed  as  having  been  con- 
tained in  it.  Thus  common  salt  is  analyzed  into  chlo- 
rine and  sodium.  Hence  we  may  say,  “ common  salt 
contains  chlorine,” — “ common  salt  contains  sodium.” 

929.  There  is  no  appeal  from  the  result  of  an  ana- 
lysis. We  may  mistake  the  name  of  the  sub-  The  certainty 
ject  analyzed,  and  also  that  of  the  element  of  Analyst, 
given  out.  But  the  things  themselves  cannot  he  mis- 
taken. The  greatest  danger  is  in  the  too  hasty  infer- 
ence from  the  analysis.  We  may  suppose  Liability  t0 
the  example  which  we  analyzed  Avas  a fair  mistakes- 
specimen  of  all  the  individuals  of  its  class,  and  con- 
tained nothing  which  Avas  not  in  them  all  and  an  essen- 
tial constituent,  Avhen  in  fact  it  was  not  so.  Hence  we 
may  predicate  of  a class  as  one  of  its  constituent  ele- 
ments that  which  was  only  a foreign  substance,  acci- 
dentally in  the  specimen  which  Ave  had  subjected  to 
our  analysis. 

930.  It  is  evident  from  these  considerations  that 
the  analysis  of  any  object  may  give  us  ele- 
ments of  its  constitution  of  which  we  were  ^element!1™! 
ignorant  before  the  analysis.  Thus  the  before  known-. 
analysis  of  water  gives  us  hydrogen  and  oxygen.  And 
it  is  especially  characteristic  of  chemical  analysis,  that 
the  elements  evolved  are  totally  unlike  the  compound 
that  was  subjected  to  the  analysis. 

931.  It  will  be  observed  that  analysis  can  give  as 
results  nothing  except  that  which  was  in  the  AnaIysis  can 
analyzed  compound.  Thus  if  we  analyze  & onpyro“,: 
water  we  get  oxygen  and  hydrogen,  and  ties- 
whatever  else  there  may  he  in  the  Avater — but  nothing 
more.  Otherwise  we  have  no  certainty  in  our  results. 


248 


LOGIC. — PAKT  II. 


[chap. 


932.  But  we  often  find  on  analysis  wliat  we  do  not 
and  cannot  find  in  analysis.  This  is  especially  true  of 
the  analysis  of  our  conceptions.  By  the  analysis  we 

it  enables  us  get  primarily  merely  what  was  contained  in 
piiesde  lp?opef  our  conception  as  the  material  properties. 
ties-  But  after  the  analysis  has  been  completed, 

we  are  able  to  contemplate  each  element  by  itself,  and 
also  their  relations  to  each  other ; and  thus  we  gain 
an  insight  of  many  implied  properties,  which  of  course 
were  not  contained  in  the  conception. 

933.  This  distinction  between  what  we  get  in  an 
analysis  and  what  we  get  on  analysis,  is  very  generally 

overlooked  or  omitted  in  speaking:  of  the 
often  overlook-  results,  lhis,  lor  instance,  is  very  constantly 
done  by  Cousin,  ivlio  is  certainly  one  of  the 
most  skilful  and  lucid  in  his  analysis  of  all  the  meta- 
physicians that  the  world  has  ever  seen. 

934.  But  as  the  conceptions  which  we  form  of 
The  results  of  objects  in  the  reality  of  being  are  liable  to 
conceptions  differ  somewhat  from  those  which  existed  in 

eriTior  different  the  Divine  Mind  before  their  creation ; and 
as  the  conceptions  which  one  mind  forms 
of  objects  in  the  reality  of  being  will  differ  somewhat 
from  those  formed  by  other  minds  of  the  same  objects, 
and  as  analysis  of  the  conception  can  give  only  what  is 
contained  in  the  conception,  the  results  of  these  analy- 
ses by  different  persons  will  be  as  various  as  their  con- 
ceptions ; agreeing  necessarily  in  some  of  their  elements 
while  they  differ  in  others. 

935.  So,  too,  that  which  may  be  expressly  contained 
Material  and  in  .one  man’s  conception  as  a material  pro- 
tie?  may  ieTb  perty  in  contingent  Matter — that  is,  material 
ent  minds.  to  his  conception,  may  be  only  implied  in 
another  and  vice  versa. 

936.  This  results  from  the  fact  that  our  minds  are 
Difference  in  imperfect  and  limited,  “ Variasse  est  error  is.” 
Analysis!"3  ° And  there  is  probably  no  intellectual  endow- 
ment in  respect  to  which  men  differ  more  than  in  their 
powers  of  analysis.  A Newton  or  a Pascal  could  see 


IX.]  METHODS  OF  INVESTIGATION. SECT.  VI.  249 

at  a glance  into  tlie  relations  and  properties  of  geome- 
trical figures,  what  men  of  ordinary  powers  can  see — 
for  to  understand  is  to  see — only  after  hours  of  study 
and  a long  process  of  demonstration.  And  to  an  infi- 
nite mind  the  result  of  the  longest  and  most  compli- 
cated calculation  must  be  as  evident  at  the  first  glance, 
as  the  first  axioms  of  Geometry  are  to  us. 

SECTION  VI. 

Of  Induction  and  Analogy. 

937.  The  words  Induction,  and  Analogy,  are  each 
of  them  used  to  denote  Methods  of  Investi-  mduction  and 
gation,  and  Methods  of  Proof  also.  In  one  ^ods^finve^tl- 
sense  of  the  word  they  are  regarded  as  fur-  gatlon  & Pr00f- 
nishing  Predicates,  in  the  other  as  proving  them  to  be 
true.  In  this  latter  sense  I shall  consider  them  in  the 
next  Chapter." 

938.  Induction  f is  the  Method  by  which  we  colli- 
gate several  facts,  having  identity  of  Formal  induction. 
Properties  as  a species,  and  in  consequence  of  these 
facts  agreeing  in  some  other  property  not  at  first  con- 
ceived as  Formal,  we  predicate  that  fact  of  all  indi- 
viduals in  that  species,  or  of  the  species  as  a whole. 

939.  But  when  the  facts  of  any  two  opposite  species 
agree  in  any  of  their  Formal  properties  (123),  Analogy, 
and  we  affirm  a predicate  of  the  second,  on  the  ground 
that  we  had  found  it  true  of  the  first,  we  call  this  the 
Method  of  Analogy.];  And  the  Method  is  said  to  be 

* Part  II.  Chap.  III.  Sect.  V. 

t Aristotle  Top.  Book  I.  Cap.  XII.  defines  Induction  to  be  r;  curb  twv 
k ad'  '4ko.(ttov  e-nd  to  KaOoSov  etpoSoi,  “ the  way  of  passing  from  particulars 
to  universals.” 

J Whately  has  defined  Analogy  as  being  a “ resemblance  of  ratios  ; ” 
and  quoted  Aristotle  for  it  \_Ki-yuv  o^aoidrij?].  But  this  definition  does  not 
seem  to  me  either  correct  or  sufficiently  definite  to  answer  any  good  pur- 
pose. We  certainly  speak  of  “facts”  as  analogous,  as  well  as  “ratios” 
or  “ relations.” 

But  is  the  analogy  in  the  relations  at  all  ? Is  it  not  in  all  cases  and 
necessarily  in  tho  facts  ? Thus  suppose  A and  B each  entertain  a similar 

11* 


250 


LOGIC. — PAHT  II. 


[chap. 


that  of  Contraries  when  we  affirm  unlike  or  contrary 
contraries.  predicates  on  the  ground  of  contrariety  of 
Formal  properties. 

040.  JSTot  only  do  many  of  the  facts  or  objects  in 
objects  in  Na-  Nature  have  such  properties  in  common,  but, 
pnmd“prope£  these  properties  are  taken  as  Formal  at  plea- 
ties-  sure,  and  thus  become  matter  determining  a 

sphere,  and  the  facts  are  subsumed  under  that  concep- 
tion. The  word  “ subsumed”  which  I have  just  intro- 
duced, has  been  pretty  extensively  used  to  denote  the 
inclusion  of  individuals  within  the  sphere  of  a con- 
ception. 

941.  But  no  sooner  do  we  find  that  we  have  thus 
other  proper-  constituted  a class  of  individuals,  by  their 

the  class  be-  subsumption  under  any  one  of  their  proper- 
mai.  ties,  than  we  find  that  there  are  other  pro- 

perties also  which  are  common  to  all  the  individuals  of 
this  class. 

942.  By  this  fact  both  science  and  memory  are 
greatly  assisted.  One  can  learn  as  quick,  remember 
as  easily  and  as  long  a general  statement  like  this : 

cias  hap  n U ^11  resinous  bodies  produce  negative  elec- 
savestimTand  tricity,”  as  lie  could  the  specific  statements 
predicating  the  same  thing  of  each  kind  of 
resin  separately ; or  even  the  individual  statements 
predicating  it  of  each  particular  piece  of  resin — the 
specific  statements  would  be  quite  numerous,  the  indi- 
viduals innumerable.  But  the  general  statement  occu- 
pies no  more  space  on  the  written  page,  and  requires 
no  more  time  in  enunciation  and  committing  to  me- 
mory, and  no  more  effort  to  retain  it,  than  each  of  the 
individual  statements  taken  separately. 

relation  to  C,  is  not  the  analogy  between  A and  B ? If  not,  Analogy  can 
answer  only  for  illustration,  and  never  for  investigation  and  proof.  We  infer 
the  relation  of  B to  C,  for  instance,  from  (1)  the  known  relation  of  A to  C, 
and  (2)  the  known  analogy  of  B to  A in  that  particular  point  which  thus 
connects  A to  C.  But  if  the  Analogy  be  in  the  relations  and  not  in  the 
facts,  the  relation  must  he  known  before  the  Analogy  ; and  hence  Analogy 
as  a means  of  investigation  or  proof  is  a vaTtpov  irpioTov,  a “ later-first,” 
or  as  some  might  prefer  to  call  it,  a Petitio  Principii. 


H.]  METHODS  OF  INVESTIGATION. SECT.  VI.  251 

913.  Hence  it  is  of  the  utmost  importance  to  science 
that  such  classifications  should  he  made,  and  ^ w b 
that  in  each  case  the  generalization  should  riedas  h.ghlb 
he  as  high — that  is,  the  sphere  of  the  subject  1>u“‘  e' 

as  comprehensive  as  the  matter  of  the  predicate  will 
allow. 

914.  But  we  see  objects  one  by  one  and  indivi- 
dually. Ho  where  are  species  and  genera  No.  direct  per- 
objects  of  direct  observation  and  intuition,  properties1'  ‘of 
W e can  never  therefore  find  any  one  of  the  cksses  as  such- 
contingent  predicates  of  a class  by  direct  intuition  of 
the  class-conception.  We  must  have  some  other  Me- 
thod of  investigating  their  properties. 

915.  We  have  three  classes  of  cases  coming  under 

what  is  commonly  called  Induction.  The  Three  cases, 

first  is  that  in  which  we  have  the  Formal  Proper- 
ties of  some  class  given  to  find  the  Modal  Proper- 
ties common  to  the  individuals  in  that  class.  Or 
secondly,  we  may  have  the  Modal  property  as  our  start- 
ing-point, and  reason  from  it  back  to  the  Formal ; and 
thirdly,  we  may  have  some  event  or  phenomenon  re- 
garded as  an  effect  to  find  the  class  of  objects  that  will 
produce  that  effect. 

916.  (1)  In  the  first  place  we  fix  upon  the  promi- 
nent and  striking  features  which  certain  facts  Giving  a class 
have  in  common.  We  give  them  a general  name- 
name,  and  have  made  the  Properties  the  Essentia  of  a 
Genus.  Then  we  group  together  other  facts  in  the 
same  way  into  another  Genus,  based  upon  plain  and 
obvious  properties  as  Essentia. 

917.  But  suppose  we  have  a Whole  to  be  embraced 
in  our  classification.  Take  for  example  the  domestic 
animals  of  a farm.  We  then  complete  the  We  complete 
classification  already  begun  by  division.  ^ by3SIdiu- 
We  refer  all  having  the  properties  which  we  sion- 

had  assumed  as  the  Essentia  of  horses,  for  instance,  to 
the  class  “ horses  ; ” all  having  the  Essentia  of  cows  to 
the  class  “ cows ; ” and  so  on  with  all  the  classes 
which  we  had  formed.  But  starting  from  the  idea  of  a 


252 


LOGIC. — PAKT  II. 


[CHAP. 


Whole,  all  the  individuals  in  that  Whole  must  he  in- 
cluded in  some  one  of  the  classes  which  were  in  the 
other  process  regarded  as  so  many  genera,  but  which 
are  now  in  this  process  regarded  as  coordinate  species. 
And  if  in  our  process  of  division  we  find  any  indivi- 
duals not  included  in  any  class  which  we  had  pre- 
viously constituted,  we  either  constitute  that 

Change  of  Pnn-  . d . . . . . . 

dpie  of  ciassi-  at  once  into  a new  coordinate  species  or 

lication.  i »«i  <■»  -1  • • • -i  -j  • <-» 

change  our  principle  ot  division,  and  classify 
on  other  differentia  than  those  with  which  we  had 
commenced. 

948.  Thus  in  all  the  Natural  Sciences  different 
()  often  done  in  principles  of  classification  have  succeeded 
sciences.11  ura  each  other  with  every  important  step  in  ad- 
vance which  the  science  has  taken.  New  discoveries 
or  a more  careful  analysis  has  brought  to  light  new 
facts  and  new  relations  of  fact  to  fact,  and  suggested  a 
better  principle  of  classification  and  nomenclature  than 
was  possessed  before.  In  Botany,  in  Zoology,  in  Crys- 
talography  such  changes  have  frequently  occurred. 

949.  Now  in  this  process  of  classification  the  For- 
mula used  is  that  described  above  (569),  in  wljich  a 

Formula  of  common  predicate  denoting  the  Essentia  of 
classification.  t]ie  Grenus  is  affirmed  of  the  individuals  com- 
prehended under  it  individually.  When  this  has  been 
done  we  give  to  the  individuals  a class-name,  and  then 
the  matter  of  this  class-conception  gives  the  limits  to 
its  sphere,  by  including  in  it  not  only  the  colligated 
individuals  which  had  been  named  in  the  process  of 
the  classification,  but  also  all  others  which  have  the 
Essentia  of  the  colligated  individuals,  and  which  con- 
stitutes the  matter  of  the  class-conception. 

950.  We  now  come  to  the  next  step  in  the  Induc- 
common  mo-  tioii.  We  find  that  several  individuals  in 
predicated11 8 the  genus  thus  formed  have  a Modal  pro- 
perty common  to  them  all,  which  however  was  not  so 
obvious  as  the  property  upon  which  our  classification 
was  based,  or  which  at  all  events  was  not  included  in 
our  class-conception.  We  then  predicate  this  property 


n.]  METHODS  OF  INVESTIGATION. SECT.  VI.  253 

of  the  individuals  in  the  class,  one  after  another  as 
above  (571),  and  then  predicate  this  property  of  the 
class  as  a whole.  And  this  deductive  judgment  affirms 
the  Modal  property  of  the  species  as  in  the  example 
given  (570). 

The  wolf  is  carnivorous  ; 

The  fox  is  carnivorous  ; 

The  cat  is  carnivorous,  &c. : 

.•.  The  Canidai  are  carnivorous. 

951.  And  when  we  have  thus  affirmed  a property  of  a 
whole  class  we  speak  of  it  as  a law  of  Nature.  General  Facts. 
It  is  in  truth,  however,  but  a general  fact,  and  wants 
much  yet  of  being  what  can  properly  be  called  a law.* 

952.  There  are  three  steps  in  Inductions  of  this  class 
which  it  will  be  well  to  notice  separately;  Three  steps  of 
not  indeed  as  involving  or  depending  upon  Indu('tl0n- 
different  principles,  but  as  being  different  and  wider 
applications  of  the  same  principle. 

953.  (a)  For  the  first  let  us  take  the  following  : 

We  learn  of  an  individual  animal  a property  which 

was  not  included  in  its  class-conception,  as  First  step, 
of  the  horse,  the  fact  that  he  sheds  his  hair  every  spring. 
We  soon  learn  of  the  next  horse  that  we  become  ac- 
quainted with,  that  he  also  sheds  his  hair  in  the  same 
way.  After  learning  this  fact  of  a number  of  indi- 
viduals in  the  species  horse,  we  predicate  the  fact  as  a 
general  fact  or  law  with  regard  to  the  species,  that 
“ horses  shed  their  hair  every  spring.” 

951.  This  may  be  regarded  as  illustrating  the  first 
and  primary  step  in  Induction.  It  is  a pro-  This  p,ocess 
cess  which  we  all  go  through  with  in  refer- 
ence  to  many  of  the  most  common  species  kn0"ledse- 
of  facts,  long  before  we  reflect  upon  the  process  at  all, 
or  study  its  laws. 

955.  (5)  Then  for  the  second  step  take  the  case  in 
which  we  extend  or  widen  our  induction  by  The  Second 
including  several  species.  Thus,  step- 


* See  Part  II.  Chap.  III.  Sec.  V. 


254 


LOGIC. PART  n. 


[CHAP. 


The  cat  has  canine  teeth  ; 

The  dog  has  canine  teeth  ; 

The  wolf  has  canine  teeth  ; 

therefore  the  dog,  and  the  wolf,  the  cat  and  all  animals 
which  have  canine  teeth  constitute  a natural  genus, 
which  we  will  call  the  Canidce. 

But  the  dog  is  carnivorous  ; 

The  cat  is  carnivorous  ; 

The  wolf  is  carnivorous  ; 

therefore  the  Canidse,  or  all  animals  with  canine  teeth, 
are  carnivorous. 

956.  (<?)  For  the  third  step  we  take  the  fact  or  law 
Third  step.  thus  developed  as  a Formal  property,  and 
constitute  upon  it  a species  of  “ Carnivorous  Animals 
and  in  the  course  of  our  investigation  we  find  that  their 
habit  of  life  is  always  accompanied  by  a peculiarity  of 
the  digestive  organs  and  alimentary  canal,  the  stomach 
being  smaller  and  the  canal  much  shorter  than  in 
herbivorous  animals.  We  have  now  established  an- 
other fact.  We  may  make  this  fact  a Formal  property 
and  proceed  with  our  investigation  as  before,  showing 
that  all  animals  with  this  kind  of  digestive  apparatus 
possess  more  energy  and  activity,  and  stand  higher  in 
the  scale  of  being,  if  we  will  measure  their  rank  by 
the  power  of  control.  Thus  the  lion  and  the  tiger, 
though  much  smaller,  control  the  elephant,  camel,  &c. 

957.  (2)  If  now  our  investigations  had  began  at  the 
The  second  other  end,  if  we  had  seen  the  animal  eating 

class:  cases  in  n 1 i 

which  we  begin  nesh,  and  so  known  that  lie  was  carnivorous 
properties.  before  we  had  discovered  the  peculiarity  ot 
liis  teeth,  we  should  have  regarded  this  Mode  as  some 
indication  of  what  could  be  found  in  the  constitution — 
that  is,  among  the  Formal  properties  of  the  animal. 
It  would  then  become  a case  for  the  investigation  of  a 
Formal  property  indicative  of  this  Mode  of  life;  the 
Method  then  becomes  the  same  as  that  for  finding  the 
Cause  when  we  have  an  effect  given.*  Canine  teeth, 


* See  the  next  Section. 


II.]  METHODS  OF  INVESTIGATION. SECT.  Vl.  255 

however,  cannot  be  regarded  as  a Cause,  notwithstand- 
ing they  may  be  the  Sign,  of  that  mode  of  life. 

958.  Having  by  this  Method  ascended  from  the 
Modal  to  the  Formal  property,  we  reverse  Having  found 
the  order  and  predicate  the  Mode  of  the  spe-  peertyor“e1  Se- 
cies upon  the  ground  of  the  Formal  property  verse  the  order, 
which  is  its  sign,  just  as  when  the  Formal  property  had 
been  our  starting-point  in  the  order  of  time. 

959.  (3)  There  are  cases  in  which  we  have  a pheno- 

menon occurring,  which  we  regard  not  as  a Third  class . 
Modal  property,  but  merely  as  an  occasional  “T" 

effect.  For  an  example  take  the  case  of  fects- 
electricity  excited  by  resinous  bodies.  The  appear- 
ance of  the  electricity  is  not  a mode  of  the  resinous 
bodies,  it  is  merely  an  effect  of  their  excitement  by 
silken  or  woollen  surfaces. 

960.  In  this  class  of  cases  the  Induction  is  scarcely 
any  thing  more  than  a classification  with  a Induction  in 
view  to  the  general  fact.  W e find  one  kind  ‘^®ely 

of  resins,  shellac  for  example,  susceptible  of  Ihin6 a cia“me 
negative  electricity.  But  we  cannot  find  in  cation 
our  analysis  of  shellac  any  thing  which  seems  to  us 
likely  to  cause  electricity,  any  thing  by  which  we  can 
predict  a priori  on  finding  the  same  property  in  sub- 
stances of  another  kind  that  they  will  excite  the  same 
kind  of  electricity.  We  soon  find,  however,  that  other 
resins  do  excite  negative  electricity,  and  thus  far  in  our 
experience  all  known  resins  agree  in  this  peculiarity. 
But  why,  or  what  is  the  property  in  them  by  which 
they  produce  an  effect  so  unlike  other  substances  under 
the  same  circumstances  we  cannot  tell.  Chemistry 
reveals  to  us  many  such  cases,  and  it  is  cpiite  possible 
that  they  point  to  something  yet  to  be  discovered,  hut 
which  is  at  present  beyond  even  the  forerunning  con- 
jectures and  hypotheses  of  science. 

961.  And  yet  when  the  nature  of  electricity  is  bet- 

ter understood  we  may  be  able  to*see  some-  Furtherknow. 
thing  in  resins— some  element  common  to  vedrftKinto 
them  all  as  a constitutive  or  Formal  principle  ln' 


256 


LOGIC. — PABT  n. 


[CHAP. 


of  the  class,  which  we  shall  then  understand  to  be  as 
naturally  adapted  to  the  production  of  that  particular 
state  of  electric  excitement  which  we  call  Negative 
Electricity,  as  the  canine  teeth  of  the  Canidge  are  to  the 
carnivorous  habit  of  life.  The  Analogies  of  Nature 
and  the  developments  and  progress  in  the  history  of 
Science  lead  us  to  expect  such  a result. 

962.  But  as  it  is,  we  place  much  less  dependence 
upon  the  inductions  of  this  class  than  upon  those  of 

These  ciassi-  either  of  the  others.  We  regard  them  in 
festive8 of  ain-  fact  as  but  mere  classifications  of  particular 
ductions.  facts  into  a General  fact,  preparatory  to  an 
induction  and  prophetic  of  it,  which,  however,  we  are 
not  fully  prepared  to  make. 

963.  In  the  course  of  our  induction  we  for  the  most 

Exceptions  be-  part  find  some  exceptions  to  the  general  fact 
Ei'aafCri0  which  we  first  deduce  in  this  way.  And  so 
Sons.  strongly  are  we  attached  to  the  fundamental 

ideas  under  which  we  pursue  any  science,  that  when 
the  exceptions  become  very  numerous  we  abandon  the 
classification  upon  which  the  induction  was  based,  and 
classify  anew  and  on  another  principle.  Thus  the  old 
philosophers  predicated  the  property  of  “ falling  ” of 
heavy  bodies  only,  such  as  earth,  stones,  metals  ; and 
they  supposed  that  light  bodies,  as  air,  vapor,  and 
smoke  belonged  to  an  opposite  class,  of  which  “ as- 
cending ” could  be  predicated  by  the  Method  of  Con- 
traries. But  it  has  been  found  that  light  bodies  also 
tend  to  the  earth,  and  now  a new  classification  has 
been  made,  and  “ falling  ” is  a property  predicated  of 
all  bodies  having  the  common  Essentia  of  being  “ un- 
supported.” And  we  state  it  as  a general  fact,  that 
“ all  bodies  left  unsupported  fall  to  the  earth.” 

961.  We  have  already  remarked  that  those  proper- 
Naturai  ciassi-  ties  upon  which  the  classification  of  natural 

fications  not  of-  x n -i  . -i-. 

ten  based  upon  geiieras  are  based,  are  not  generally  those 
ties.  which  are  subject  to  comparisons  of  inten- 

sity, as  color,  size , density , &c.,  among  material  pro- 
perties ; virtue,  wisdom,  courage,  &c.,  among  spiritual 


H.]  METHODS  OF  INVESTIGATION. — SECT.  VI. 


257 


properties,  but  ratlier  those  which  do  not  admit  of  any 
such  comparison.  In  the  case  just  given,  bodies  either 
are  or  are  not  supported.  If  one  is  supported,  it  re- 
mains where  it  is,  if  not,  it  falls.  We  take  no  notice 
of  the  fact  of  the  support  being  adequate  to  sustain  a 
body  many  times  as  large  ; that  fact  has  no  bearing 
upon  the  classification  or  the  deduction  based  upon  it. 
ISTor  if  there  be  something  under  it  which  is  not  suffi- 
cient to  support  it,  do  we  take  notice  of  that  fact — the 
body  is  simply  “ unsupported.” 

965.  But  in  the  previous  classification  in  which  it 
was  affirmed,  that  “ all  heavy  bodies  fall,”  the  classifi- 
cation was  based  upon  a property  which  admits  of 
comparisons  of  intensity.  Bodies  are  more  or  less 
heavy.  “Heavy”  and  “light”  are  not,  like  “sup- 
ported ” and  “ unsupported”  contraries,  but  they  are 
simply  sub-contraries  / and  the  Induction  based  upon 
that  classification  was  fallacious.  It  stated  the  truth, 
indeed,  but  not  the  whole  truth ; and  the  suppressio 
veri  was  for  all  purposes  of  science  just  as  bad  as  a 
false  statement. 

966.  Analogy  stops  short  of  an  Induction  of  the 
second  degree  (955),  because  for  the  most 

part  the  objects  of  the  class  to  which  the  an  incomplete 
inference  is  drawn — that  is,  the  subject  of 
the  Conclusion  is  beyond  the  reach  of  actual  Observa- 
tion and  Experiment.  But  if  we  could  investigate  the 
individual  to  which  we  reason  by  analogy,  we  should 
convert  such  Analogy  into  an  Induction  of  observed 
facts  in  the  same  species. 

967.  In  all  the  Inductive  Sciences  there  are  many 
of  the  fields  of  inquiry  from  which  by  the 

nature  of  the  case  we  are  excluded,  and  extemno5  Ss 
there  are  others  which  neither  our  telescopes  "nducuon" hc'is 
nor  our  microscopes  can  reach.  In  such 
cases  Analogy  is  our  only  guide  and  furnishes  our  only 
light — a light  indeed  of  inestimable  value,  but  still  a 
light  which  needs  to  be  most  cautiously  followed.  In 
the  anatomy  of  the  human  frame,  for  instance,  we  have 


258 


LOGIC. PAJRT  II. 


[CHAP. 


tlie  facts  for  an  induction  before  us.  But  in  physiology 
and  biology  many  of  tlie  facts  are  such  that  they  never 
can  be  brought  under  inspection  and  observation. 
Comparative  Anatomy,  however,  has  shown  an  analogy 
between  man  and  animals  ; and  we  may  often  subject 
them  to  an  examination  into  the  functions  of  reproduc- 
tion, life  and  death,  which  we  can  never  make  in  the 
case  of  man. 

968.  All  substances  are  brought  by  their  Formal 
relation  to  the  laws  and 
Thus  bodies  that  are 


The  Formal  properties  into 

Properties  of  all  x x t*  , 

species  bring  sequences  ot  nature, 
field  of  Analogy,  transparent,  are  by  this  property  connected 
with  an  important  class  of  phenomena  and  laws  in 
optics.  Resinous  bodies,  by  a property  common  to 
them  all,  but  which  has  no  distinctive  name,  are  con- 
nected with  the  science  of  electricity  in  one  way  ; and 
vitreous  bodies,  by  a property  common  to  them,  are 
connected  with  the  other  kind  of  electricity.  Iron  by 
a peculiar  property  is  capable  of  important  magnetic 
phenomena,  and  the  laws  of  terrestrial  polarity. 
Dense  bodies,  by  their  density,  are  connected  with  the 
laVs  of  gravitation.  Opaque  bodies,  by  their  opacity, 
with  reflection  of  light  and  the  phenomena  of  color. 
Thus  every  Formal  property  of  a body  connects  it  with 
some  general  law  or  fact — some  class  of  phenomena 
more  or  less  comprehensive ; and  those  relations  are 
the  basis  of  the  natural  genera  and  species  upon  Avhi'ch 
all  science  and  all  knowledge  depends. 

969.  Each  property  of  a body  is  thus  connected  in 
the  concatenation  of  nature’s  laws  and  sequences,  with 
some  law  and  with  some  phenomenon,  which  as  a con- 
sequent is  regarded  as  an  effect  or  a mode. 

970.  Row  when  in  such  a natural  species  we  find 
one  property  which  is  regarded  as  Formal,  connected 

with  a certain  law  and  producing  certain 
effects,  we  infer  by  analogy  that  any  indi- 
vidual in  another  species,  having  the  same  Formal 
property,  must  sustain  a like  relation  to  that  law,  and 
have  the  same  modal  property  or  effect. 


Application  of 
Analogy. 


XI.]  METHODS  OF  INVESTIGATION. — SECT.  VII.  259 

971.  Thus  the  physician  knows  that  a certain  drug 
is  a deadly  poison  to*  some  of  the  animal  tribes.  He 
infers  from  analogy  between  the  animal  and  By  the  Medical 
man  that  it  will  prove  so  to  man.  He  knows  Prac“tio,,er- 
that  there  are  many  points  of  identity  between  man 
and  the  animals — they  have  an  Essentia  in  common  ; 
he  knows  that  most  drugs  produce  the  same  effects 
upon  men  as  upon  animals.  But  with  regard  to  this 
particular  drug’s  influence  upon  man,  or  whether  man 
and  beast  are  identical  in  that  particular  property,  in 
consequence  of  which  that  drug  is  a deadly  poison  for 
the  beast — he  knows  nothing  anterior  to  experience  of 
its  effect  upon  man  except  what  he  can  infer  from  the 
analogy  between  the  man  and  the  beast. 

SECTION  VII. 

Of  Elimination. 

972.  The  facts  of  Nature  have  not  only  a lateral 
connection,  so  to  speak,  by  which  they  admit  Thg 

of  classification  into  Genera  and  Species,  Nature  have  re” 
with  a view  to  general  facts  and  laws,  but  cedent  and  con- 
each  one  had  something  before  it  which  is  sequen ' 
regarded  as  its  Cause,  and  will  be  followed  by  some- 
thing which  will  be  regarded  as  its  Effect. 

973.  Causality  is  not  a property  inhering  in  any 
substance  that  can  be  cognized  by  any  of  the  Causali(y  not 
senses.  We  can  see  antecedence  in  time,  ceHlrtV>lt- 
but  the  causality  is  a matter  of  inference.  selt: 

974.  Causality , however,  is  something  more  than 
mere  antecedence  and  necessary  connec-  causality some- 
tion.*  Day  and  night  follow  each  other,  mi?fmoantecen- 
tlie  successive  steps  of  the  pedestrian,  the  dence- 

* The  Fallacy  which  we  sometimes  hear  spoken  of  as  the  Fallacy  of 
post  hoc  ergo  propter  hoc , consists  in  inferring  that  because  one  event  is  after 
another,  therefore  it  was  caused  by  that  other.  Bishop  Latimer  exposes 
this  fallacy  in  some  who  attributed  the  laxity  of  morals  in  his  time  to  the 
Reformation,  by  narrating  the  anecdote  of  a countryman  who  accounted 


260 


LOGIC. — PAET  II. 


[CHAP. 


days  of  the  week,  the  months  of  the  year,  all  succeed 
each  other,  and  yet  no  one  supposes  that  each  is  the 
Effect  of  that  which  preceded  or  the  Cause  of  that 
which  follows.  So  the  antecedence  is  a fact  in  the 
reality  of  being ; the  causality,  where  there  is  any, 
belongs  to  the  reality  of  truth  alone.  It  seems  to  direct 
the  thought  into  the  unseen  realities  of  truth  ; and  the 
Reason,  by  an  intuition  peculiar  to  itself,  sees  there 
what  is  not  expressed  in  the  sensible  properties  of  ex- 
ternal objects. 

975.  By  means  of  Induction  we  may  always  find 
the  Invariable  Antecedent  in  the  phenomena  of  Nature, 
invariable  An-  But  the  distinction  between  a mere  Antece- 

dent  and  a Cause,  is  what  no  processes  of  a 
duction.  posteriori  investigation  can  give.  It  is  some- 
thing which  the  Reason  superadds  to  the  results  of  our 
investigation  in  certain  cases,  just  as  in  Induction  the 
Reason  superadds  that  which  distinguishes  a General 
Law  from  a mere  General  Fact.  By  the  insight  which 
Induction  enables  us  to  get  into  the  Class-conceptions 
and  Final  Causes  of  the  Creator,  we  are  enabled  to 
affirm  the  concomitance  of  certain  properties  of  objects 
as  Laws  arising  from  that  physical  necessity  which  is 
based  upon  the  volitions  of  the  Divine  Will.  So,  too, 
by  Induction  we  establish  certain  antecedences  and 
consequences  in  Nature  as  general  facts,  upon  which 
the  Reason  infers  or  rather  superadds  the  relation  of 
Cause  and  Effect. 

976.  All  investigation  of  Causes  must  of  course  end 
The  causes  in  at  last  in  the  Absolute  or  First  Cause  (108). 

cMdaTy0"'1  SIJ  But  the  Method  which  we  are  now  describ- 
ing must  proceed  step  by  step,  and  from  an}'  one  fact 
or  event  it  can  give  us  only  that  which  next  preceded 
it  in  the  order  of  time  and  of  causality.  This  becomes 

for  the  sands  that  obstructed  the  Goodwin  Harbor — by  the  building  of  Ten- 
terden  Steeple — “There  were  no  sands,”  said  he,  “in  the  harbor;  that  is, 
none  that  gave  trouble,  until  just  after  the  steeple  was  built  on  Tenterden 
Church.”  Hence  the  good  people  of  Tenterden  supposed  that  the  steeplo 
had  caused  the  sands  in  their  harbor. 


II.]  METHODS  OF  INVESTIGATION. SECT.  VII. 


261 


in  its  turn  an  Effect  to  be  investigated  in  like  manner, 
until  in  like  manner  “ omnia  exeunt  in  Deum  ” (all 
things  lead  to  God).  Then  and  then  only  do  we  find 
an  Efficient  Cause  for  the  facts  and  phenomena  of 
Nature. 

977.  This  results  from  the  fact  that  Matter  is  always 
regarded  as  inert,  and  incapable  of  acting  And  Instru. 
except  as  it  is  acted  upon.  Even  the  im-  mentaI- 
ponderable  agents,  heat,  light,  electricity,  &c.,  can 
hardly  be  regarded  as  exceptions  to  this  rule.  As  yet 
we  know  not  what  they  are.  But  the  Reason  refuses 
to  regard  them  as  any  thing  more  than  means,  Instru- 
mental or  Second  Causes  in  the  hands  of  an  Intelligent 
or  First  Cause. 

978.  Our  inquiry  into  Causes  therefore  can  be  only 
an  investigation  into  the  antecedents  of  any 

event,  along  which  the  mind  conceives  that  dit.ons  required 
the  efficiency  which  brought  that  event  into  by  lhe  Rtason' 
the  reality  of  being  may  have  passed.  And  the  only 
conditions  which  the  Reason  imposes  are,  (1)  that  that 
which  is  to  be  regarded  as  a cause  be  an  invariable 
antecedent ; (2)  that  it  be  a true  cause  ; and  (3)  that  it 
be  a sufficient  cause  [causa  vera  and  causa  suffi- 
cient 

979.  Of  the  first  we  need  say  no  more  than  the  self- 

evident  proposition,  that  a cause  must  pre-  First;  Antece- 
cede  its  effect  in  point  of  chronology.  dence  in  Time. 

980.  Of  the  second,  we  can  only  say  that,  a true 
cause  must  be  a substance  acting  through  second: a suh- 
some  of  its  properties.  A mere  state  or  mode  stanGe- 

of  a substance  is  no  cause,  although  of  course  it  will 
often  be  an  antecedent.  Thus  “ day  ” is  a mere  mode  of 
light,  and  is  no  cause  of  the  succeeding  mode  A Mode  no 
which  we  call  “ night.”  One  of  the  steps  of  a proper  Ciiuse- 
pedestrian  is  merely  one  condition  or  stage  in  his  pro- 
gress, and  no  cause  of  the  succeeding  one.  “Day” 
and  “ step  ” are  not  substances  in  the  metaphysical 
sense  of  the  words  at  all  (Part  I.  55  and  note),  but 
merely  modes  or  stages  of  certain  substances.  Thus 


262 


LOGIC. — PART  II. 


[chap. 

the  step  that  crushes  the  worm  cannot  be  regarded  as 
tlie  cause  of  the  crushing.  Not  the  step  but  the  man 
Mho  steps  is  the  cause  ; and  the  word  “ step  ” denotes 
substantive*  merely  the  accidental  condition  or  mode  in 
Modal  causes.  wi1ic]1  the  cause  happened  to  be  when  it 
exerted  its  efficiency.  It  may  be  well,  therefore,  for 
the  sake  of  having  a name,  to  call  the  former  the  Sub- 
stantial or  Substantive  Causes,  and  the  latter  the  Modal 
Causes. 

981.  But  not  only  must  the  antecedent  which  we 
are  to  regard  as  a cause  be  a substance,  in  order  to  be 

cause  must  a vera  causa , it  must  also  bear  some  propor- 
porfiosnmteopriti  ti°n  or  relation  to  the  effect  in  order  to  be  a 
Effect.  sufficient  cause,  or  causa  sufficiens.  Thus, 
a boil  on  one’s  hand  may  be  a vera  causa  of  a good 
deal  of  pain  and  annoyance,  but  it  would  not  be  re- 
garded as  a sufficient  cause  of  the  death  of  an  indi- 
vidual, if  one  having  such  a sore  should  be  found 
dead. 

982.  The  substantiality*  (38)  of  causes  must  be  af- 

firmed by  an  ultimate  intuition  of  the  Mind  itself.  One 
The  substan-  can  110  more  prove  that  a “ day  ” is  no  sub- 
uit!mateesintub  stantial  cause  than  that  the  sun  is  round,  or 
tlon-  a rose  is  red.  If  our  faculties  do  not  so  see 

these  objects,  there  is  no  help  for  us  in  one  case  any 
more  than  in  the  other.  The  fault  is  an  individual  in- 
firmity, and  can  he  regarded  as  requiring  no  diminu- 
tion of  the  confidence  which  all  persons  whose  faculties 
are  in  their  normal  condition  are  entitled  to  place  in 
the  exercise  of  those  faculties. 

983.  But  the  sufficiency  of  causes  in  Nature  is  what 

The  sufficiency  we  can  learn  only  from  observation.  Of 
Nature11  learned  Primary  Causes,  as  of  the  Infinite  Mind,  and 
tionand^fndul:  °f  the  human  mind,  from  the  very  conception 
tmn.  0f  them  we  can  predicate  certain  events  or 

phenomena  as  effects.  We  know  that  Infinite  Wisdom 

* When  we  speak  of  a cause  as  being  necessarily  a substance,  we  must 
be  understood  as  speaking  not  of  mere  antecedence,  but  of  causality.  An 
antecedent  need  not  be  a substance,  but  a cause  must. 


II.]  METHODS  OF  INVESTIGATION. SECT.  VII. 


263 


will  know  all  things — Infinite  Power  can  do  all  things, 
that  Mind  or  Reason  can  understand,  that  Will  can 
choose,  and  determine  the  formal  character  of  actions. 
And  so  in  Mature  we  may  predicate  a priori,  on  the  class- 
conception  of  certain  objects  something  of  their  conca- 
tenation in  the  antecedents  and  consequences  of  Mature. 
But  this  class-conception  is  itself  obtained  a posteriori , 
and  the  nature  and  efficiency  of  their  causality  is  a 
part  of  that  which  we  learn  by  observation,  and  through 
which  we  are  enabled  to  arrive  at  this  class-conception. 
It  is  certainly  very  possible,  and  perhaps  we  had  bet- 
ter say  that  it  is  probable,  that  the  causality  of  all 
objects  was  an  element  in  the  class-conception  which 
preceded  in  the  Divine  Mind  the  act  of  their  creation. 

981.  In  the  sufficiency  of  causes  we  have  two  dis- 
tinct elements  to  take  note  of — the  adequacy  Sufficiency  of 
in  amount  and  homogeneity  in  kind.  Thus  Cause  includes 

. . nr*  • . ° n • , • .•  two  Elements. 

wine  is  the  sufficient  cause  of  intoxication. 

But  a single  wine-glassful  would  be  inadequate  in 
quantity.  But  if  one  should  attribute  a scarlet  fever 
or  the  small-pox  to  the  use  of  wine,  he  would  mistake 
the  homogeneity  of  the  cause  to  the  effect  which  ho 
ascribes  to  it.  Wine  is  a cause,  a vera  causa , and  a 
causa  sufficiens  of  a variety  of  phenomena,  hut  not  of 
the  diseases  just  named. 

985.  As  every  cause  must  he  a substance,  and  every 
substance  is  known  only  by  its  properties,  so  also  it  is 
known  only  as  existing  in  some  certain  con-  causality  often 
dition  or  mode  ; and  this  condition  or  mode  ft*  mode  0fth“ 
is  often  inseparable  from  that  antecedence  Substance- 

to  the  effect  which  renders  the  substance  a cause  of  it. 
Thus  wine  is  a cause  of  intoxication  only  when  taken 
into  the  stomach  and  in  a certain  quantity.  The  Air 
is  a cause,  but  it  causes  the  uprooting  of  trees,  and  the 
other  effects  of  tornadoes  only  when  it  exists  in  the 
mode  of  violent  motion. 

986.  Hence  we  have  four  classes  of  words  Four  classes 

, i i j j of  words  used 

or  terms  winch  are  used  to  denote  causes : — to  denote  cau- 
(1)  Simple  words  denoting  substances,  as  se8' 


264: 


LOGIC. — PAKT  II. 


[chap. 


“ heat,”  “ electricity,”  “’light,”  &c.,  substances  whose 
efficiency  as  causes  is  always  active  wherever  the  sub- 
stances themselves  are  found ; then  (2)  we  have  such 
words  as  denote  merely  the  condition  or  mode  in  which 
the  cause  exerts  its  influence,  as  when  we  say  that 
“ walking  fatigues  one,” — “ the  succession  of  day  and 
night  causes  great  changes  in  the  temperature,”  &c. 
Then  we  have  (3)  those  complex  terms  which  express 
both  the  cause  and  the  mode  or  condition  upon  which 
the  production  of  the  effect  depends,  as  “ the  spake 
falling  upon  gunpowder  caused  the  explosion.”  Or 
sometimes  (4)  we  have  single  words  which  in  them- 
selves express  the  substance  and  its  modes,  as  “ earth- 
quake,” “ hurricane,”  “ lightning,”  &c. 

987.  Words  or  terms  in  order  to  express  a cause 
adequately  should  always  he  of  this  last-named  kind. 

The  last  kind  They  should  express  not  only  the  substance 
Seadequate6  which  is  the  cause,  but  also  the  mode  or 
ly-  condition  on  which  the  efficiency  as  cause 

is  exerted. 

988.  The  immediate  Antecedent  of  any  phenomena 
simple  and  will  sometimes  he  complex,  consisting  of 

cedents.  several  elements,  and  at  others  simple.  Thus 
Heat  is  a simple  antecedent.  It  admits  of  no  phy- 
sical analysis.  But  the  sun — a burning  lamp — acidi- 
fying vegetable  matter — the  mixing  of  sulphuric  and 
nitric  acids — are  all  complex  antecedents,  compound- 
ed of  the  simple  antecedent  or  cause,  heat,  among 
others. 

989.  We  must  remember  also  that  in  regard  to 
many  of  the  compound  facts  in  Nature,  as  elsewhere, 

The  Causality  the  causality  is  not  to  be  found  in  any  one 
Spon  theepceoms  of  the  ingredients  or  elements  alone  and  by 
piexity.  itself.  Thus,  it  is  not  the  charcoal,  nor  the 
nitre,  nor  the  sulphur  which  causes  the  explosion  when 
a spark  falls  upon  that  combination  of  these  three  ele- 
ments which  constitute  what  is  called  gunpowder. 
Neither  of  those  elements  are  explosive  alone  and  by 


265 


n.]  METHODS  OF  INVESTIGATION. SECT.  VII. 

itself.*  Not  any  property  of  either  of  the  substances, 
therefore,  is  the  cause  of  the  explosion — the  combina- 
tion itself  is  the  cause. 

990.  When  therefore  the  combination  is  the  cause, 
and  not  any  one  of  the  simple  elements  in  that  combina- 
tion, the  complex  antecedent  is  to  be  regarded  No  E,imina. 
as  the  cause.  But  it  is  often  the  case 'that  wTelfthe™^6 
some  one  element  in  the  complex  antecedent  theepconml 
may  be  the  cause,  and  it  will  in  many  cases  r’  exity- 

be  found  of  the  greatest  importance  to  ascertain  which 
of  the  simple  elements  in  any  complex  antecedent  is 
the  real  cause  of  the  phenomena  which  we  are  investi- 
gating. 

991.  For  this  purpose  several  Methods  have  been 
resorted  to,  which  have  "been  called  Methods  Elimination, 
of  Elimination.  They  consist  in  removing  entirely  or 
varying  in  quantity  certain  of  the  elements  in  any 
complex  antecedent  or  consequent  for  the  purpose  of 
ascertaining  its  relation  to  the  supposed  Consequent  or 
Antecedent. 

992.  Elimination  depends  upon  the  four  following 
axioms : 

(1.)  No  two  simple  causes  will  produce  the  same 
effect  and  the  converse.  Hence  identity  of  First  Axiom, 
effect  implies  identity  of  cause,  and  diversity  of  effect 
implies  diversity  of  cause. 

993.  Several  complex  antecedents  may  be  followed 
Ixy  fhe  same’  effect".  Thus  a wax-taper,  an  oil-lamp>,  a 
coal-fire,  the  concentrated  .-.rays  of  the  sun,  may  each 
be  the  cause  of  the  melting  of  sealing-wax.  But  in 
these  complex  antecedents,  there  is  identity  in  one  sim- 
ple element  “ heat,”  by  which  the  effect  is  produced. 

99d.  And  so  strong  is  the  belief  in  this  axiom  of 
identity  of  cause,  where  there  is  identity  of  effect, 

* This  has  recently  been  disputed  in  regard  to  Nitre.  But  I believe 
that  its  explosiveness  has  not  been  proved.  But  even  if  it  has  it  will  not 
affect  the  propriety  of  the  illustration ; since  if  it  is  explosive  at  all,  it  is 
not  explosive  under  any  such  circumstances  as  those  contemplated  in  the 
text. 


12 


266 


LOGIC. — PAKT  II. 


[chap. 


that  scientific  men  cling  to  it  even  when  facts  seem  to 
influence  of  he, against  them,  and  the  belief  in  its  infalli- 
llle  bmlndsupof  bility  has  often  led  by  means  of  an  analysis 
men-  of  the  complex  antecedent  to  the  discovery 

of  what  would  otherwise,  perhaps,  never  have  been 
suspected  to  ejist.  And  in  investigations  of  the  phe- 
nomena of  Electricity,  Galvanism,  and  Magnetism,  the 
identity  of  effects  produced  in  many  cases  have  led 
very  generally  to  the  belief  that  these  forces  are  but 
one  and  the  same  thing,  acting  in  different  ways  and 
under  different  circumstances.  Nay,  so  far  has  this 
matter  gone,  that  it  has  been  suggested  that  this  one 
cause  “ Electricity,”  if  that  be  the  name  of  it,  is  the 
cause  of  heat  and  light,  and  the  medium  through  which 
the  mind  exerts  its  control  over  the  body. 

995.  As  we  know  nothing  a posteriori  of  substances 
except  through  their  properties,  so  we  know  nothing 

Axiom  proved  of  causes  as  causes — that  is,  nothing  of  the 
a priori  causality  of  objects  in  Nature,  except  by 
inference  from  their  effects.  As  we  have  already  said, 
a cause  must  be  a substance,  it  must  be  adequate  and 
homogeneous  to  its  effect.  And  as  the  identity  of  ob- 
jects in  Nature  depends  upon  the  identity  of  their 
inseparable  properties,  so  the  identity  of  causes  as 
such  must  depend  upon  that  which  constitutes  their 
adequacy  and  homogeneity  to  the  effect  produced. 
Hence  the  proposition  already  laid  down,  “ the  identity 
of  effect  implies  identity  of  simple  cause.” 

996.  (2.)  The  second  axiom  is,  that  if  the  cause  is 
second  Axiom,  removed  the  effect  will  disappear.  Other- 
wise we  should  have  an  effect  without  a cause,  which 
is  absurd. 

997.  (3.)  The  magnitude  of  the  effect  varies  with 
Third  Axiom,  and  is  determined  by  the  magnitude  or  in- 
tensity of  the  cause.  Otherwise  we  should  have  some 
portion  of  causation  without  any  effect,  or  some  por- 
tion of  effect  without  a cause. 

998.  (4.)  And  fourthly,  that  cceteris paribus  the  same 
Fourth  Axiom,  cause  will  always  produce  the  same  effect. 


n.]  METHODS  OF  INVESTIGATION. — SECT.  VII.  267 

999.  The  effect  always  depends  very  much  upon 
the  substance  or  matter  upon  which  the  cause  exerts 
its  force.  Thus  heat  expands  iron,  and  con-  p Efficiency  de- 
tracts clay  ; and  as  has  been  said,  u what  is  subject  matter1! 
one  man’s  meat  is  another’s  poison.” 

1000.  This  leads  us  to  mention  the  fact  that  Con- 
sequents as  well  as  Antecedents  are  complex  consequents  ai- 
also,  and  as  such  the  result  of  more  than  IL£?emp ex  or 
one  simple  cause.  Thus,  for  example,  an  eclipse  of  the 
Moon,  considered  in  its  essence  as  an  eclipse,  and  in 
its  modes  as  occurring  on  such  a moment  and  visible 
only  at  such  a place  on  the  Earth’s  surface,  is  a com- 
plex result,  caused  by  the  various  forces  of  the  diverse 
attractions  of  the  different  heavenly  bodies.  In  this 
case  the  cause  of  the  eclipse  was  one  thing,  the  cause 
of  its  occurring  at  precisely  that  moment  rather  than 
another,  or  so  as  to  be  visible  on  one  part  of  the  Earth’s 
surface  rather  than  another,  are  each  of  them  different 
causes,  and  may  be  called  Formal  Causes.  In  this  case, 
however,  we  use  the  name  Formal  Cause  in  a sense 
somewhat  different  from  what  we  have  given  to  it  in 
reference  to  logical  classifications,  and  yet  not  so  dif- 
ferent as  to  occasion  any  confusion  or  error. 

1001.  Let  us  now  proceed  to  consider  the  several 
Methods  of  Elimination.  Of  these  we  may  Five  Methods 
have  five  that  are  specially  useful,  arising  of  Eliminatl0n' 
out  of  the  axioms  already  mentioned  as  applied  to  the 
different  cases  which  may  arise  for  investigation. 

1002.  The  first  law  of  Elimination  in  the  order  in 
which  I shall  name  them  is  the  following  : 

(1-)  By  the  Elimination  of  any  one  element  in  the 
complex  antecedent , its  appropriate  conse-  First  Method. 
quent  or  effect  will  disappear  also. 

1003.  Thus  suppose  a physician  administers  a pre- 
scription consisting  of  three  ingredients,  camphor,  and 
morphine,  and  ipecac — and  finds  unpleasant  illustration, 
symptoms  ensue  that  can  be  ascribed  to  nothing  but 
the  dose  which  he  had  prescribed.  Suppose  now  that 
he  administers  two  of  the  ingredients  without  the  third, 


268 


LOGIC. — PART  n. 


[CHAR. 

or  the  two  combined  with  some  others,  and  the  un- 
favorable symptoms  do  not  ensue,  he  would  doubtless 
ascribe  those  symptoms  as  an  effect  to  that  ingredient 
in  the  dose  which  in  the  second  administration  he  had 
omitted. 

1004.  (2.)  When  there  is  a uniform  disagreement 
second  Method,  in  several  Antecedents  in  ail  the  elements 
except  one,  that  one  must  be  regarded  as  the  cause  of 
any  unvarying  element  in  the  Consequents  of  those  di- 
verse Antecedents. 

1005.  Thus  suppose  we  have  an  Antecedent  A, 
illustration.  consisting  of  elements  x,  y,  and  s,  and  a 
Consequent  C.  If  now  we  can  form  or  avail  ourselves 
of  new  combinations  as  w x and  v,  or  s x and  t , having 
x alone  common  to  them  all,  and  the  Consequent  C 
following  in  each  case,  Ave  should  have  no  doubt  that 
A is  the  cause  of  C,  by  reason  of  its  element  x. 

1006.  Such  cases  occur  not  unfrequently  in  Chem- 

of  use  in  chem-  istry,  when  we  have  to  deal  with  agents 
macy.  which  we  either  cannot  get  in  a separate 

and  pure  state,  or  if  we  could  their  use  would  be  in- 
convenient or  unsafe.  The  same  thing  holds  true  also 
in  Medical  practice.  Some  of  the  most  indispensable 
of  the  medical  agents,  in  fact  nearly  all  of  those  that 
are  the  most  efficient  can  never  be  used  except  in 
combination  with  others.  Hence  their  effect  can  be 
ascertained  only  by  forming  them  into  different  com- 
binations, varying  in  each  experiment  every  other 
ingredient. 

1007.  (3.)  By  diminishing  or  increasing  the  cause, 
Third  Method,  a corresponding  increase  or  diminution  of  the 
effect  will  ensue. 

1008.  This  law  of  Elimination  supposes  a case  in 
which  the  element  in  the  compound  Antecedent  cannot 
be  wholly  eliminated. 

1009.  Thus  “ heat  ” is  an  agent  of  this  kind.  There 
illustration.  is  no  absolute  of  cold  or  total  absence  of 
heat.  But  we  can  increase  or  diminish  the  intensity 
of  heat  to  a very  great  extent.  Thus  we  find  that 


n.]  METHODS  OF  INVESTIGATION. SECT.  VII.  269 

nearly  all  bodies  expand — become  liquid,  and  finally 
vapor,  and  even  gas,  under  intense  beat ; and  in  tbe 
absence  of  heat  all  bodies  contract,  condense,  and  be- 
come solid.  lienee  heat  is  assumed  to  be  the  cause  of 
fluidity.  The  same  may  be  said  of  density.  There  is 
no  body  without  some  density  ; and  as  the  gravitation 
of  bodies,  so  far  as  we  can  ascertain,  varies  with  their 
density — we  assume  that  density  is  the  cause  of  the 
gravitation  of  bodies,  or  that  all  bodies  gravitate  in 
proportion  to  the  quantity  of  matter. 

1010.  (T)  If , from  any  pair,  consisting  of  a complex 
Antecedent  and  a complex  Consequent , we  Fourth  Metnod. 
separate  the  elements  in  the  Antecedent , whose  effects  in 
the  complex  Consequent  are  known,  and  find  an  element 
in  the  Consequent  whose  cause  is  not  contained  in  the 
Antecedent , it  is  called  a Residual  Phenomenon,  for 
which  a cause  must  be  sought. 

1011.  We  have  many  cases  in  which  the  several 
elements  of  a complex  Antecedent  have  been  Residuai  phe- 
so  far  examined,  as  that  their  effects  both  in  nomena- 
quality  and  quantity  in  the  Consequent  are  known, 
and  yet  something  remains  to  be  accounted  for.  The 
return  of  a Comet  may  be  regarded  as  such  In  the  retura 
an  effect.  Row  among  the  causes  which  Comets- 
determine  its  return  we  know  many — the  attraction  of 
the  Earth,  the  attraction  of  the  Sun,  and  of  each  of  the 
other  heavenly  bodies  to  which  it  approaches  in  its 
path  near  enough  to  be  influenced  by  them.  These 
different  attractions  are  the  elements  in  the  cause  of 
its  return,  considered  as  a complex  Consequent,  in- 
cluding its  return  at  a precise  day  and  hour,  &c.  If 
now  we  begin  and  abstract  from  the  Cause  each  ele- 
ment, deducting  from  the  Consequent  also  its  appro- 
priate effect — appropriate  both  in  character  and  in 
amount,  in  quality  and  quantity,  and  after  thus  ab- 
stracting each  element  in  the  Cause  with  its  element  in 
the  effect,  we  find  something  remaining  in  the  effect 
still  unaccounted  for— we  have  what  Sir  John  F.  W. 
Herschel  called  a Pesidual  Phenomenon.  Thus  if  we 


270 


LOGIC. — PART  n. 


[chap. 

have  Antecedent  compound  of  a,  b,  c,  and  d ; and  Con- 
sequent consisting  of  w,  x , y , 2,  and  s ; and  abstracting 
a from  the  Antecedent  removes  w , b removes  x ; c,  y ; 
and  d,  z.  We  have  s remaining  as  a Residual  Pheno- 
menon, for  which  a cause  is  yet  to  be  sought,  and  to 
he  added  to  our  enumeration  of  the  elements  a,  b,  c, 
and  d in  the  Antecedent.  For  the  elements  in  any 
Cause  must  be  adequate  to  the  Effect,  and  the  whole 
of  it  both  in  Substance  and  in  Form. 

1012.  The  existence  of  a resisting  medium  filling 
all  space,  and  yet  so  rare  as  not  to  exert  any  perceptible 

influence  upon  the  motions  of  the  planets 
of  a resisting  and  satellites  of  our  system,  has  been  sup- 
as  a Residual  posed  to  have  been  discovered  as  a Residual 
1 henomeno".  ppenomenorij  effected  by  means  of  this  Me- 
thod in  accounting  for  the  return  of  comets  at  a period 
somewhat  less  than  that  assigned  them  by  the  calcula- 
tions of  astronomers.  But  whether  there  be  such  a 
medium  or  not,  the  Residual  Phenomenon  shows  that 
there  is  some  agency  at  work  of  which  as  yet  we  pos- 
sess no  satisfactory  knowledge,  and  which  will  need  to 
be  investigated  before  the  science  of  Astronomy  will 
be  complete. 

1013.  (5.)  Again  and  finally,  there  may  sometimes 
a doubt  arise  as  to  which  of  the  two  phenomena  are 
Necessity  for  a f°  he  regarded  as  cause  and  which  as  effect. 
Fifth  Method,  qqulSj  p js  always  observed  in  cases  of  snow- 
storms, that  just  as  the  snow  begins  to  fall  the  mercury 
in  the  thermometer  rises  a little.  Row,  is  the  change 
in  the  temperature  the  cause  or  the  effect  of  its  begin- 
ning to  snow  ? In  thunder-storms,  a flash  of  lightning 
is  sometimes  attended  by  an  increase  in  the  quantity 
of  rain  that  is  falling ; which  is  cause  and  which  is 
effeef? 

1014.  In  many  of  these  cases  we  can  answer  from 
The  doubt  set-  our  knowledge  of  the  nature  of  the  plieno- 
cases  by  a pri-  mena  themselves.  And  there  are  many 

0? 'i  knowledge  . -i  . i i • ? 

of  causes.  cases  m which  we  can  make  no  experiments 

of  Elimination.  But  when  elimination  can  be  made, 


n.]  METHODS  OF  INVESTIGATION. — SECT.  VH.  271 

the  case  comes  under  the  second  axiom.  Hence  we 
have  as  the  fifth  rule  of  Elimination, 

1015.  (5.)  Remove  one  of  the  phenomena,  and  if  the 
other  disappears  also , that  which  was  re-  Fifth  Method. 
moved  is  the  cause  and  the  other  is  the  effect.  Rut  if 
the  other  does  not  disappear,  that  which  was  removed 
was  the  effect  and  not  the  cause. 

1016.  For  an  illustration  of  this  law  it  is  very  com- 
mon to  refer  to  the  case  of  Dr.  Wells’  researches  into 
the  phenomena  of  dew.  It  was  found  in  the  illustration, 
course  of  his  experiments  that  those  surfaces  on  which 
dew  collected,  were  colder  than  those  upon  which  there 
was  none.  But  which  was  the  cause  and  which  the 
effect,  the  cold  or  the  dew  ? By  substituting  metal 
surfaces,  which  do  not  easily  become  cold  in  the  posi- 
tion in  which  he  placed  them,  for  glass,  which  being  a 
bad  conductor  does  easily  become  cold,  he  found  that 
the  glass  surfaces  and  not  the  metal  were  covered  with 
dew,  whence  he  inferred  that  the  cooling  of  the  surface 
was  the  cause  of  the  dew,  and  not  the  dew  the  cause 
of  the  cooling  of  the  bedewed  surface. 

1017.  Having  in  these  ways  learned  the  nature  of 
objects  considered  as  causes,  we  can. often  Reasoning  from 
reason  or  investigate  into  the  future  from  into  the  future, 
causes  to  their  yet  undeveloped  effects.*  Reasoning- 
in  this  Method,  however,  is  always  attended  with  some- 
thing of  danger.  W e seldom  thoroughly  comprehend 
all  the  properties  of  a Cause,  or  the  influences  which 
may  be  exerted  upon  its  efficiency  by  its  combination 
with  other  causes.  Nor  can  we  ever  see  far  enough 
into  the  future  to  enable  us  to  take  into  our  account  all 
of  the  contingencies  that  may  arise  to  modify  the  course 
of  events.  Thus  we  can  predict  the  fall  of  an  unsup- 
ported body  from  our  knowledge  of  the  law  of  gravita- 
tion. But  another  law,  as  magnetism  or  electricity,  &c., 


* This  has  also  been  called  “ reasoning  a priori." — Whately’s  Rhetoric, 
Part  I.  c.  II.  32.  It  is  not,  however,  a priori  in  the  sense  in  which  wo 
nave  thus  far  used  these  words. 


LOGIC. — PART  n. 


272 


[chap. 


may  interpose  between  the  cause  and  the  effect  and 
break  the  connection. 

1018.  But  yet  there  are  many  cases  in  which  this 
sometimes  our  is  the  only  Method  by  which  we  can  pene- 
torecaTti’ng16  the  trate  the  future.  The  astronomer  reasons 
1 in' Astronomy,  upon  it  in  predicting  the  rise  and  set  of  the 
sun,  the  changes  of  the  moon, .the  recurrence  of  eclipses, 
comets,  conjunction  of  the  stars,  &c.,  &c.  And  he  feels 
perfect  confidence  in  bis  conclusions. 

1019.  The  chemist  reasons  in  this  Method  when  he 
In  Chemistry.  designs  an  experiment.  He  knows  the  ef- 
fects which  certain  agents  as  causes  generally  produce, 
lie  reasons  from  this  knowledge  to  the  eflect  which 
those  agents  will  produce  in  the  new  case,  and  trusts 
to  this  calculation  to  produce  the  test  or  crisis  which 
he  wishes  to  determine  by  his  experiment. 

1020.  The  physician  reasons  on  this  principle  when 

m Medicine,  lie  prescribes  his  remedies,  and  looks  for  the 

desired  change  in  the  condition  of  the  patients  as  the 
effect  of  what  he  had  prescribed. 

1021.  The  legislator  has  to  rely  on  this. Method  in 
in  Legislation,  the  discharge  of  his  duties,  as  legislator,  to  a 
very  great  extent.  It  is  often  his  only  guide  in  devis- 
ing' laws  and  institutions  for  the  welfare  of  those  for 
whom  he  is  called  upon  to  legislate.  And  the  causes 
whose  influence  he  has  to  calculate,  are  moreover  often 
of  the  subtlest  and  most  evanescent  or  incomprehensi- 
ble character. 

1022.  It  will  have  been  observed  from  the  fore- 
Reasoning  from  o;oin it  remarks — that  in  speaking  of  the  cause 
limited.  oi  any  tact  or  event,  we  reier  to  a compound 
object  within  which  one  element  alone  was  causal  of 
the  eflect.  Hence  reasoning  from  effect  to  cause,  we 
can  reason  only  to  that  element,  and  not  to  any  one 
of  the  combinations  into  which  it  may  enter.  Thus 
heat  is  the  cause  of  fluidity.  If  now  we  start  from 
fluidity,  as  an  eflect,  we  can  argue  to  the  existence  of 
heat  as  a cause.  But  as  this  heat  may  have  been  pro- 
duced by  the  sun,  by  a spirit-lamp,  by  a chemical 


n.]  METHODS  OF  INVESTIGATION. SECT.  VII. 


273 


decomposition,  by  friction,  &c.,  &c.,  we  cannot  argue 
to  the  reality  of  any  one  of  those  combinations  of  heat 
from  the  mere  fact  of  fluidity.  Hence  we  can  investi- 
gate and  argue  much  more  specifically  from  cause  to 
effect  than  from  effect  to  cause. 

1023.  In  some  of  the  most  important  inquiries 
which  we  can  have  to  make,  however,  we  Limited  ,-n 
have  no  other  Method  that  we  can  pursue, 
but  that  from  effect  to  cause.  In  Medical  Effect  10  cause, 
diagnosis,  for  instance,  this  is  for  the  most  part  the 
only  means  of  ascertaining  the  nature  of  the  disease  to 
be  cured. 

1021.  The  -physician  is  called  to  see  a patient — the 
prominent  symptom  is  we  will  suppose  a illustration, 
headache — this  is  an  effect  which  may  proceed  from  a 
variety  of  causes.  If  it  were  the  first  case  of  headache, 
and  had  never  been  investigated,  there  would  be  no 
other  Method  that  could  be  pursued  with  success  than 
those  we  have  already  described.  But  in  the  present 
state  of  the  science  almost  all  causes,  and  varieties  of 
causes,  have  been  investigated.  The  causes  which 
may  produce  such  results  are  pretty  well  known  and 
recorded. 

1025.  Each  cause  also,  for  the  most  part,  produces 
some  other  effects  also  besides  the  one  that 

is  chiefly  conspicuous ; and  no  two  causes  Antecedent  has 

J i , t • i n o several  Effects. 

ever  produce  effects  which  are  all  of  them 
precisely  alike  in  all  respects.  Hence  the  physician  is 
to  look  for  the  other  effects,  or  “ symptoms,”  as  he 
will  call  them,  until  he  finds  one  or  more  that  is  pecu- 
liar to  one  of  the  causes  of  headache.  This  one 
becomes,  what  Bacon  proposed  to  call  an  experimen- 
tum  crucis,  or  a test  fact.  And  in  the  pur-  E!£P„imentum 
suit  of  such  a test,  he  will  often  find  it  neces-  crucis- 
sary  to  experiment  with  tests  voluntarily  applied,  as 
well  as  to  observe  the  facts  that  already  exist  without 
his  procurement. 

1026.  In  our  attempt,  to  reason  into  the  future  of 

12* 


274 


LOGIC. — PART  n. 


[CHAP. 


human  conduct,  however,  the  moral  freedom  of  man 
Reasoning  from  and  the  uncertainty  as  to  the  determinations 
inaUMomiGMa?  °f  will,  render  our  conclusions  pecu- 
ter-  liarly  liable  to  error.  Investigation  or  rea- 

soning in  this  way,  however,  is  much  more  reliable 
when  applied  to  masses  than  when  applied  to  a single 
individual  (800,  801). 


HI.]  METHODS  OF  PROOF  AND  REFUTATION. SECT.  I.  275 


CHAPTER  IH. 

OF  METHODS  OF  PROOF  AND  REFUTATION. 


SECTION  I. 

Of  Proof. 

1027.  Methods  of  Proof  presuppose  both  terms  of 
the  Proposition,  whereas,  as  we  have  s.een,  Methods  of 
Investigation  presuppose  merely  the  Subject.  By 
Proof,  then,  we  mean  the  establishment  of  the  proof. 
Copula,  affirming  or  denying  the  relation  between  the 
given  Subject  and  Predicate.  From  what  has  been 
said  (131),  it  is'  evident  that  no  proof  is  required  of 
Intuitive  Judgments.  Hence  in  all  our  inquiries  into 
Methods  of  Proof,  we  are  understood  to  have  reference 
to  the  Proof  of  Deductive  Judgments  only. 

1028.  In  the  preceding  Part  of  this  Treatise,  we 
have  examined  the  ways  in  which  Cognitions  and  Judg- 
ments can  be  so  combined  as  to  serve  as 

Means  of  Proof.  We  have  here  now  to  con-  u^Ahe  F°r. 
sider  the  ways  in  which  these  Means  or  For- 
mula may  be  used,  with  an  especial  reference  to  the 
Matter  on  which  they  are  to  he  used. 

1029.  I have  already  remarked  that  Methods  of 
Investigation  are,  to  some  extent,  Methods 

ot  Proof  also.  In  Investigation  we  expect  vesication  to 
to  find  as  the  result,  that  with  which  we  start  Methods ex  A 
as  a Proposition  in  Methods  of  Proof.  But  Fl00t  al>0' 
besides  being  thus  in  respect  to  Methods  the  converse 


276 


LOGIC. PAJRT  II. 


[chap. 


of  each  other,  their  Differentia  as  Alternate  Species  of 
Methods  is  as  stated  above ; the  one  gives  (Whately 
would  say  proves)*  the  Major  Terms,  and  the  other 
proves  the  Copula. f 

1030.  Methods  of  Proof  may  he  either  direct  or 
Direct  and  in-  indirect.  Direct  Methods  prove  the  Propo- 

oiriw!ethods  sition  to  be  established ; the  Indirect  prove 
its  contradictory  to  be  untrue,  from  which  we  have  the 
desired  Proposition  by  Immediate  Inference. 

1031.  Direct  Proof  is  effected  by  whatever  Means 
Direct  proof,  or  in  whatever  Method,  wherever  we  show 
that  the  Subject  of  the  Proposition  has  or  has  not  the 
essential  matter  of  the  Predicate.  Since  whatever  has 

* Rhetoric,  Part.  I.  Chap.  I.  § 1. 

f We  have  in  popular  use  the  words  Induction  and  Deduction,  which 
are  understood  to  denote  Methods  of  Proof  the  reverse  of  each-  other.  Both, 
however,  may  he  regarded  as  Methods  of  either  Investigation  or  of  Proof, 
since  even  Deduction  may  give  a new  Major  Term  for  a subject  (see  Part 
II.  Chap.  III.  Sec.  III.)  ; and  the  word  Induction  is  also  used  to  denote  a 
Method  of  proving  the  truth  of  the  generalization  which  it  effects.  But 
the  contrast  between  the  two  Methods  in  the  common  estimation  just 
referred  to,  is  between  Induction  and  Deduction  as  Metlwds  of  Investigation. 
No  contrast  or  comparison  between  the  former  as  a Method  of  Investiga- 
tion, and  the  latter  as  a Method  of  Proof,  would  ever  be  made  with  any 
view  to  a disparagement  of  either  Method.  The  contrast  for  the  disparage- 
ment of  “ the  Deductive  Method,”  as  it  is  called,  was  undoubtedly  occa- 
sioned by  the  misuse  of  it  as  a Method  of  Investigation,  which  seems  to 
have  had  its  origin  to  some  extent  at  least  in  the  “ Organon ” of  Aristotle; 
and  was  encouraged  by  the  schoolmen  and  philosophers  generally  until  the 
time  of  Bacon,  the  famous  author  of  the  “ Novum  Organon.” 

But  there  is  no  occasion  for  such  a contrast.  Induction  as  a Method 
of  Proof  is  itself  deduction  from  the  very  necessities  of  the  case,  as  we  shall 
see  in  our  inquiry  into  the  grounds  of  its  validity  as  a Method  of  Proof. 
But  regarded  as  Methods  of  Proof,  Induction  and  Deduction  differ  in  one . 
of  their  more  obvious  properties  whioh  has  not  yet  been  mentioned. 

In  Deduction  the  General  Principle  or  Major  Premise  is  most  conspi- 
cuous and  will  be  made  most  prominent.  In  Induction  the  particular  facts 
or  cases — that  is,  the  Minor  Premise  is  made  the  most  conspicuous.  So 
that  Deduction  and  Induction  are  both  of  them  for  the  most  part  made  by 
means  of  Enthymemes  ; the  former  suppressing  the  Minor  and  the  latter 
the  Major  Premise.  In  Deduction  the  inclusion  of  the  Minor  Term  or 
Subject  of  the  Syllogism  in  the  Subject  of  the  Major  is  considered  too  ob- 
vious to  need  express  statement.  In  Induction  the  general  principle  of  all 
Induction — the  uniformity  of  Nature  is  assumed  as  too  obvious  and  un- 
disputed to  require  explicit  recognition. 


HI.]  METHODS  OF  PROOF  AND  REFUTATION SECT.  I.  277 


the  Essentia  of  any  class,  is  of  necessity  included  in  that 
class,  and  vice  versa.  To  render  Direct  Proof  possible, 
therefore,  two  conditions  are  necessary: — itstworequi- 
(1)  that  the  Proposition  to  be  proved  must  sites- 
have  a Positive  Term  for  its  Predicate ; and  (2)  that 
there  may  be  a conception  occupying  a middle  posi- 
tion in  Logical  Quantity  between  its  Subject  and  its 
Predicate. 

1032.  Without  this  last  condition  the  Proposition 
must  be  either  intuitive  (131),  or  incapable  of  proof. 

1033.  Thus  for  the  first  case — Every  Effect  has  a 
Cause.  This  is  something  more  than  a simple  Propo- 
sition in  A,  as  stated  ; for  it  results  from  the  Jud„ment- 
nature  of  the  Matter,  that  whatever  has  a wit^noMiddie 
cause  is  an  effect.  Hence  the  Subject  “ every 
Effect,”  and  the  Predicate  “ has  a Cause,”  are  coex- 
tensive spheres,  and  both  distributed.  Hence  there 
can  be  no  Middle  Term  in  Logical  Quantity  between 
them.  The  one  is  not  included  in  any  species  which 
is  comprehended  by  the  other.* 

1031.  For  the  second  case,  take  any  Proposition 
which  affirms  what  is  not  true,  as  “ apples 
are  gingerbread.  It  is  seen  at  once  that  capable  of 
although  these  articles  may  be  made  coor- 
dinate species  in  a comprehending  genus,  as  “food” 
for  instance,  yet  in  no  way  can  one  of  them  be  made 
to  be  a comprehending  sphere  to  the  other,  and  conse- 


* We  may,  however,  need  to  have  the  terms  of  an  Intuitive  Judgment 
defined  or  explained  before  the  mind  can  assent  to  them.  This  processs, 
however,  is  not  to  be  mistaken  for,  or  confounded  with,  proof  of  the  Proposi- 
tion expressing  the  judgment.  Thus  in  the  case  above  given,  one  would 
hesitate  at  the  judgment  until  he  might  obtain  an  adequate  conception  of 
what  we  mean  by  “ cause,”  and  what  by  “ effect.”  In  that  case  he  would 
be  in  want  rather  of  instruction  than  of  proof. 

And  such  in  fact  will  be  the  case  universally  when  one  of  the  terms  is 
but  a synonyme  of  the  other,  or  both  are  but  alternate  conceptions  of  the 
same  subject  (460).  In  this  case  the  Syllogism  which  we  may  construct  is 
rather  for  instruction  than  proof,  designed  to  explain  our  terms  rather  than 
to  prove  that  the  Predicate  may  be  affirmed  of  the  Subject  of  the  Con- 
clusion. 


278  LOGIC. — PART  n.  [chap. 

quently  there  can  be  no  conception  coming  between 
them  in  Logical  Quantity. 

1035.  Without  the  first  condition,  namely,  that  the 
propositions  Proposition  to  be  proved  must  have  a Posi- 

predicatc!atlve  tive  Term  for  its  Predicate,  there  can  be  no 
direct  proof,  since  Positive  Terms  only  denote  their 
spheres  by  their  matter  (131).  Hence  if  the  Predicate 
be  not  Positive  it  has  no  matter,  or  rather  it  gives 
none,  by  which  we  can  determine  whether  the  given 
Subject  be  included  in  it  or  not. 

1036.  The  Indirect  Proof  depends  upon  the  Prin- 
indirect  proof,  ciple  of  Excluded  Middle  (100),  and  is  ac- 
complished by  proving  the  falsity  of  the  contradictory 
of  that  which  we  wish  to  prove.  But  as  the  contra- 
dictory of  an  Affirmative  is  always  Negative,  the  Indi- 
rect Method  is  seldom  used  to  prove  Affirmatives, 
except  in  three  classes  of  Propositions,  which  do  not 
admit  of  the  direct  Method  ; namely,  (1)  Intuitive 
Judgments ; and  (2)  those  in  which  the  words  “ infi- 
nite ” and  “ eternal,”  &c.,  are  used  as  Predicates  ; or 
(3)  Affirmative  Propositions  with  Negative  Predicates. 

1037.  It  has  commonly  been  held,  that  Axioms 
Axioms  inca-  expressive  of  Intuitive  Judgments  a priori , 

rect  proof.  are  incapable  ot  proof  ibis  must  be  under- 
stood of  Direct  Proof  only — for  of  Indirect  Proof  they 
all  admit.  It  consists  in  this  case  in  showing  that  the 
May  be  proved  contradictory  violates  either  the  Principle 
indirectly.  0f  Identity  (122),  and  Contradiction  (123), 
or  of  Sufficient  Cause  (125).  If  it  violates  the  first  it 
destroys  the  Subject  (781  and  note ) ; if  the  second,  it 
involves  an  absolute  scepticism  or  unbelief,  by  im- 
peaching the  veracity  of  our  means  of  knowledge.  It 
thus  removes  the  very  foundation  upon  which  we  can 
pretend  to  know  any  thing ; and  so  the  very  ground 
upon  which  we  would  base  the  assertion  by  which  we 
seek  or  expect  to  accomplish  our  object.  Thus  if  one 
denies  the  proposition,  “ the  foliage  is  green,”  he 
asserts  a proposition  contradictory  to  the  sense  of 
sight,  concerning  matter  in  regard  to  which  we  have 


nr.]  METHODS  OF  PROOF  AND  REFUTATION. — SECT.  I.  279 

absolutely  no  means  of  knowledge  but  the  sense  of 
sight.  Hence  if  that  sense  cannot  be  relied  upon,  his 
assertion  cannot  he  relied  upon,  and  we  know  nothing 
of  colors.  And  so  of  all  other  propositions  asserting 
the  primary  sense-perceptions. 

1038.  The  words  “ eternal  ” and  “ infinite ,”  have 
been  sometimes  regarded  as  Negatives.  At 

others  they  are  claimed  as  Positive.  But  for  infinite" use<iaas 
all  the  purposes  of  deduction,  they  can  be  lredlcJtli3 
used  only  as  though  they  were  negatives.  They  pre- 
dicate of  the  Subject  no  essentia,  except  the  absence  of 
bounds  or  limits  in  Continuous  Quantity.  — Hence 
“ eternal,”  “ infinite,”  Negative  and  Privative  Terms 
generally,  are  all  in  the  same  category.  Denoting  no 
sphere  by  means  of  its  essence,  they  can  be  proved  of 
a Subject  only  by  the  Principle  of  the  Excluded  Mid- 
dle. We  predicate  of  the  Subject  the  Positive  Term, 
which  is  coordinate  to  the  Privative  or  Negative,  and 
thus  show  that  it  has  not  the  Essentia  of  that  Positive. 
Thus  if  we  say,  “ Space  is  infinite,”  we  sup-  lllustrated  . 
pose  that  space  is  “ finite,”  or  “ has  a limit ; ” reference  u>  the 
that  is,  a limit  in  Continuous  Quantity.  If  word  bvau' 
so,  beyond  or  outside  of  this  limit  space  is  not  or  it  is 
not  space.  But  even  if  it  is  occupied  by  material  sub- 
stance, it  is  still  space ; and  we  have  space  occupied 
and  space  unoccupied.  Hence  the  judgment  that  that 
which  is  outside  of  any  limit  is  not  space,  is  a contra- 
diction in  terms.  If  it  be  not  space,  there  is  no  such 
£ outside  of  the  limits.”  Hence  as  the  Proposition, 
“ space  is  finite,”  is  absurd,  a contradiction  in  terms — 
its  contradictory,  “ space  is  infinite,”  must  be  true. 
In  the  same  way  all  Affirmative  Propositions  with 
Negative  or  Privative  Predicates  must  be  proved  (429). 

1039.  If,  however,  the  Predicate  be  a Positive  Term, 
and  the  Copula  Negative,  we  still  have  the  positive  pre- 
Essentia  of  the  Predicate  given,  and  must  inJu^|; 
prove  that  the  Subject  has  not  that  Essentia,  ments- 

if  so  be  it  has  not,  by  either  Observation,  Testimony, 
Analysis,  or  the  Abscissio  infiniti ; since  none  of  the 


280 


LOGIC. — PAUT  II. 


[CHAP. 


other  Methods  of  Investigation  give  negative  results 
directly,  or  in  any  other  way  than  by  Immediate  Infer- 
ence on  the  ground  of  the  Excluded  Middle.  We  can 
neither  count,  nor  measure,  nor  average  what  is  not. 
Induction,  Analogy,  Example,  and  Elimination  are  all 
based  upon  the  properties  which  the  objects  of  inquiry 
do  possess,  and  not  upon  those  which  they  do  not. 

1040.  But  Testimony  comes  at  last  to  Observation 
and  Authority.  The  Abscissio  is  based  upon  Observa- 

proved  only  tion  and  Analysis.  And  Analysis  of  Objects 
Ayutoosr!ty,atioSr  's  based  upon  Observation ; and  Analysis 
Analysis.  0f  Conceptions  upon  the  Intuitions  of  the 
Reason.  Hence  in  the  last  analysis  of  our  means  of 
proving  Negative  Propositions  with  Positive  Terms  for 
Predicates,  we  have  Observation,  Authority,  and  An- 
alysis— Methods  which  give  both  the  Predicate  and 
the  Copula  in  the  one  act  and  at  the  same  time. 

It  is  a question  which  it  will  often  be  important  to 
have  answered,  when  are  we  to  regard  any  Proposition 
as  proved  ? 

1041.  Most  Premises  will  be  Conclusions  of  pre- 
premises  fur  vious  Syllogisms  ; that  is,  they  will  be  tliem- 

DeductfveJud^  selves  but  Deductive  Judgments  — and  so 
merns.  lead  us  consider  the  Premises  from  which 
they  are  deduced. 

1042.  But  there  can  be  no  infinite  retrogression. 
There  must  We  must  come  at  last  to  something  that 

p?es.,rst  nnu"  cannot  be  proved  (directly),  simply  because 
there  is  no  Middle  Term  that  can  come  between  its 
Subject  and  Predicate  by  Avhich  it  can  be  proved. 
Such  are  Axioms  or  Intuitive  Judgments.  When  we 
have  got  back  to  these  the  mind  is  satisfied, 
satisfied  with  The  question,  Why  ? which  always  implies 
a belief  in  an  anterior  judgment,  will  and 
can  be  no  longer  asked.  The  judgment  is  intuitive, 
and  affirmed  by  all  minds  as  soon  as  the  cognitions 
of  which  it  is  composed  are  apprehended  by  the 
mind.  . 

1043.  Yet  in  practice  we  seldom  need  to  go  through 


ni.]  METHODS  OF  PROOF  AND  REFUTATION. — SECT.  II.  281 

this  whole  process.  "We  may  always  assume  something 
as  known  and  admitted — something  as  hav-  Inpracticewe 
ing  been  already  proved  to  the  satisfaction  ”educ«£eJud“ 
of  those  whom  we  address  ; and  which,  con-  ments- 
sequently,  like  the  succeeding  theorems  in  Mathematics, 
are  as  certain  to  those  who  have  been  over  them  tho- 
roughly, as  the  ultimate  axioms  and  facts  themselves. 

1041.  But  as  we  have  seen  already  (186),  it  is  un- 
important whether  we  come  to  an  ultimate  pactg  and 
fact,  or  to  an  Intuitive  Judgment  or  Axiom ; ^fe°^tore|°Icvt; 
for  the  fact  can  always  be  transferred  into  a other- 
judgment  by  predicating  of  its  sphere,  any  one  of  its 
properties  which  we  wish  to  make  the  Major  Term  to 
a Syllogism. 

SECTION  n. 

Of  Demonstration. 

1045.  The  words  “ Demonstration  ” and  “ demon- 
strate ,”  are  often  used  in  popular  language,  popular  sense 
with  reference  to  the  absolute  certainty  of  Son.  emonb  ra 
the  conclusion,  rather  than  to  denote  the  method  of 
argument  by  which  it  has  been  attained. 

1046.  Demonstration,  however,  in  the  proper  sense 
of  the  word,  is  that  Method  of  Proof  in  which  Jrict  se„se  0f 
we  establish  the  truth  of  a Proposition  by  the  word- 
means  of  the  matter  necessarily  contained  in  the  con- 
ception of  its  subject.  Hence  the  Predicate  must  always 
be  either  (1)  a Material  Property,  in  which  case  the 
Proposition  expresses  an  Intuitive  Judgment  which  is 
analytic  a priori  j or  (2)  an  Implied  Property — and  in 
that  case  the  Proposition  represents  a Deductive  Judg- 
ment which  is  synthetic  a priori. 

1047.  In  each  case  the  judgment  is  a priori,  and 
implies  an  analysis  of  the  conception.  In 

the  first  case  it  affirms  what  is  given  in  the  Analysis,  "and 
analysis  ; and  in  the  second  it  affirms  what  Intuitive  Judg- 
is  seen,  on  analysis,  to  be  implied  in  the  mat-  mentb' 
ter  of  the  conception.  And  the  judgments  at  each 


282 


LOGIC. — PAKT  II. 


[CHAP. 


step,  from  the  analysis  to  the  conclusion  must  he  intui- 
tive ; and  of  course  capable  of  proof,  on  the  Principle 
of  Identity  and  Contradiction. 

1018.  In  practice,  however,  we  for  the  most  part 
use  of  pre-  adopt  a previously  made  analysis  of  the  con- 
tions.s  ception  ; and  instead  of  taking  each  of  the 
steps,  one  by  one,  we  adopt  the  results  of  previous 
demonstrations.  Thus  in  the  successive  Theorems  in 
Geometry,  we  adopt  the  results  of  the  analysis — -that 
is,  the  Definition — given  in  the  first  two  or  three  pages  ; 
and  in  each  successive  theorem,  we  adopt  as  our 
starting-point  some  proposition  proved  in  a preceding 
theorem. 

But  beside  the  Analysis  of  Conceptions  we  have 
also  the  meaning  of  words,  or  force  of  terms , as  it  is 
sometimes  called,  furnishing  us  the  matter  for  demon- 
strations. 

1049.  The  force  of  terms  or  names  is  often  very 
Arguments  great  in  determining  our  conceptions  of 

or  Terms.  things,  and  m contributing  to  our  stock  ot 
knowledge.  Most  names  instead  of  being  an  arbitrary 
sign  for  the  representation  of  things,  have  an  • etymolo- 
gical force  or  meaning  from  which  we  can  draw  some 
inference  as  to  the  idea  which  they  are  designed  to 
convey — the  conception  of  the  thing  itself,  which  was 
in  the  mind  of  the  persons  who  first  gave  the  name  to 
the  thing.  This  is  sometimes  called  the  Argument  or 
Inference,  ex  vi  termini.  It  is  however  strictly  demon- 
strative. 

1050.  Demonstrations,  ex  vi  termini , may  be  based 
Based  upon  the  either  (1)  upon  the  necessary  matter  of  the 
etymotogy  ot  a term^  or  upon  its  etymology,  or  (3)  the 

common  acceptation  of  its  meaning. 

1051.  We  have  already  seen  (212),  that  whatever  is 
On  the  neces-  contained  necessarily  in  a term  may  be  pre- 
the  term.  dicated  of  that  term.  Thus  it  is  ex  vi  termini 
that  a triangle  has  three  angles — that  a quadruped  has 
four  feet,  &c. 

1052.  And  universally  the  Essentia  of  any  class, 


m.]  METHODS  OF  PROOF  AND  REFUTATION. — SECT.  II.  283 

considered  as  a genus,  may  be  predicated  of  any  indi- 
vidual of  that  genus.  In  necessary  matter 
this  ground  ot  predication,  moreover,  extends  tween  neces- 
to  all  the  properties  which  are  common  to  tmgent  matter 
the  class  ; as  from  the  nature  of  the  matter  m thI° re“pect' 
there  can  here  be  no  exceptions  to  a general  rule — all 
triangles  must  have  three  angles  and  three  sides — and 
the  sum  of  their  angles  must  be  equal  to  two  right 
angles,  &c. 

1053.  But  in  Contingent  Matter  this  ground  of 
Demonstration  must  be  regarded  as  most  strictly  lim- 
ited to  the  Essentia  of  the  class.  Otherwise  it  might  be 
applied  to  an  exception  from  the  general  rule  and  result 
in  error. 

1054.  When  this  argument  is  based  upon  the  ety- 
mology of  the  word,  we  must  take  heed  to  the  changes 
which  words  undergo  in  their  signification, 

by  lapse  of  time  or  the  peculiar  circurn-  based®  on  Ety. 
stances  of  their  use.  Thus  allegiance  is  ad  mo'°®y  unsafe' 
legem , to  the  law.  But  if  one  should  argue,  ex  vi  ter- 
mini, that  therefore  it  does  not  bind  him  to  his  king  or 
chief  magistrate,  he  would  err  about  as  widely  as  if  he 
should  argue  that  because  Mr.  Mason  is  Speaker  of  the 
House  of  Representatives,  he  is  the  man  who  does  all 
the  speaking  in  the  House. 

1055.  The  conclusive  force  of  this  argument  is  of 
course  still  less,  where  it  is  based  upon  the 

mere  common  acceptation  ot  the  meaning  ot  on  the  common 
terms.  Such  meanings  are  otten  given  or  words  stm more 
taken  very  much  at  hap-hazard,  or  varied  s0' 
when  they  have  once  been  given  by  very  insignificant 
and  accidental  circumstances. 

1056.  In  order  to  the  absolute  certainty  which  the 
Demonstration  is  capable  of  producing,  it  is 
necessary  that  there  be  no  mistake  in  regard  an  absolute  cer- 
to  the  Material  or  Essential  Properties  of  the  u"u>’ 
Conception  from  which  we  demonstrate.  And  in  Ma- 
thematics there  is  for  the  most  part  no  difference  of 
opinion  in  regard  to  them,  and  of  course  no  possibility 


284 


LOGIC. — PAKT  II. 


[CHAP. 


of  mistake  ; the  essential  properties  of  a triangle,  or  a 
circle  are  the  same  in  the  estimation  of  all  men.  Every 
class-conception  of  necessity  has  such  properties. 
Reason  why  it  But  in  the  class-conceptions  which  we  form 
fn " n c o ri  tin  gent  of  objects  in  the  reality  of  being,  there  is 
Matter.  always  also  some  contingent  matter  includ- 
ed ; and  hence  there  will  be  diversity  in  the  estimates 
which  men  will  form  of  the  properties  included  in 
tlie  conception  — some  regarding  those  as  essential, 
which  others  will  regard  as  merely  accidental  and 
contingent.  In  this  fact  is  great  liability  to  error,  and 
the  great  source  in  fact  from  which  errors  in  Demon- 
stration proceed. 

1057.  We  must  also  remember  that  a property 
which  is  only  accidental  to  the  conception  of  an  object 

for  one  purpose,  may  become  essential  to  its 
perties  become  conception  tor  another.  lx  ig  ht-angledness , 
for  example,  is  accidental  to  the  conception 
of  triangle,  but  essential  to  the  conception  of  the  class 
or  species  which  we  call  “ right-angled  triangles  P So 
“unsupportedness”  is  purely  accidental  to  the  concep- 
tion of  ponderable  bodies.  But  it  is  an  essential  pro- 
perty of  the  class-conception,  formed  for  the  purpose 
of  investigating  and  proving  the  fact,  and  the  law  of 
gravitation. 

1058.  And  as  a general  rule,  we  may  say  that  any 
General  Rule,  property  by  means  or  on  account  of  which 
we  may  include  its  substance  in  any  predicate,  is  an 
essential  property  in  the  conception  which  we  form 
of  that  subject  with  reference  to  the  use  of  that  pre- 
dicate. 

1059.  When  we  enlarge  the  matter  of  any  class- 
increasing  the  conception,  and  thereby  narrow  its  sphere 

ter,  enlarges  the  by  taking  into  our  class-conception  another 
monstrauon.  as  a Material  property,  we  are  enabled  to 
proceed  still  farther  and  demonstrate  still  other  implied 
properties,  which  have  been  brought  in  by  means  of 
the  newly  admitted  Material  property.  Thus,  suppose 
to  the  Material  properties  of  triangle,  which  are  two, 


nr.]  METHODS  OF  PROOF  AND  REFUTATION. SECT.  II.  285 


three-sidedness  and  three-angledness , we  add  the  one 
more,  right-angledness.  We  now  have  a narrower  sphere, 
but  we  are  able  to  demonstrate  many  properties  of 
right-angled  triangles — the  species — which  we  could 
not  demonstrate,  and  which  were  not  true  of  triangles — 
the  genus  merely. 

1060.  But  besides  Mathematics,  a large  part  of  As- 
tronomy, Mechanics,  and  what  are  called  Demonstration 
the  Mixed  Sciences  generally,  are  largely  in  a11  Sciences- 
indebted  to  Demonstration.  The  same  is  true  in  Logic, 
in  Ethics.  These  are,  and  of  necessity  must  be  to  a 
very  great  extent,  if  not  wholly  a priori  and  demon- 
strative sciences. 

1061.  Logic  has  especially  been  called  “ the  Mathe- 
matics of  Thought.”  And  in  Logic,  as  in  in  Logic. 
Mathematics,  we  must  prove  the  legitimacy  and  force 
of  both  our  Formulae  and  our  Methods  a priori,  before 
we  are  entitled  to  place  any  confidence  in  the  Conclu- 
sions or  results  to  which  they  may  lead  us. 

1062.  We  have  already  remarked  that  Arithmetic, 
Algebra,  and  the  Calculus,  are  but  Methods  of  Inves- 
tigation in  Discrete  Quantity  (883).  But  we 

are  obliged  to  justify  the  Methods  by  De-  b^fustmelTby 
monstrations.  Take  the  Rule  of  Addition,  Demonstratlon- 
of  Subtraction,  of  Multiplication,  of  Division,  of  Invo- 
lution or  Evolution,  or  the  Binomial  Theorem,  or  any 
other,  and  we  see  at  once  that  they  are  but  Methods 
of  finding  results.  But  the  Methods  are  all  justified  a 
priori , by  inferences  from  the  Necessary  Matter  of  the 
Conception  ; that  is,  from  the  Material  Properties  of 
the  Methods  themselves.  We  say,  for  example,  that 
the  square  of  any  Binomial,  as  a + 5,  is  the  square  of 
the  first  term  plus  twice  the  product  of  the  two,  plus 
the  square  of  the  second,  or  a?  + 2 ab  + 1> 2.  And  this  is 
shown  to  be  true  from  the  nature  of  the  Process  or 
Method  itself,  as  will  be  seen  by  a reference  to  any 
treatise  on  Algebra,  where  the  Binomial  Theorem  is 
discussed. 

1063.  So  in  Ethics.  We  lay  it  down  as  a rule  that 


286 


LOGIC. — PART  n. 


[chap. 


the  communications  between  man  and  man  should  be 
Demonstration  based  upon  veracity  and  benevolence.  We 
in  Ethics.  prove  it  from  the  class-conception  of  society, 
having  proved  or  assumed  that  man,  as  a species,  can 
live  only  in  society.  Thus,  suppose  the  contrary,  that 
deception  and  hate  were  the  conditions  or  laws  of 
human  association.  Deception  and  hate  would  destroy 
society,  not  only  by  rendering  association  among  men 
impossible— hut  hate  would  take  the  life  of  man,  begin- 
ning with  the  weakest  and  most  defenceless,  until  only 
one,  and  he  the  strongest,  were  left  alive.  But  one 
does  not  make  “ society .”  Hence,  on  the  principle  of 
contradiction  (422),  we  affirm  veracity  and  benevolence 
to  be  necessary  rules  of  morality. 

1064.  The  same  holds  true  of  all  class-conceptions 

in  every  department  of  knowledge.  There  are  certain 
Demonstration  properties  not  contained  but  implied  in  the 
ments’ofknow-  class-conception,  which  may  be  predicated 
ledge.  0f  every  individual  comprehended  under  that 

conception.  I have  instanced  the  laws  of  Motion  as 
predicable  on  the  class-conception  of  Matter  (791). 

1065.  In  Theology,  also,  we  may  predicate  “ sin  ” 
of  the  class-conception,  man,  as  a being  having  the 

illustration  power  of  choice,  finite  in  capacity,  sur- 
from  Theology,  rounded  py  objects  of  desire,  some  of  which 
are  prohibited. 

1066.  How  in  every  department  of  knowledge,  just 
sciences  be-  in  proportion  as  our  class-conceptions  be- 

of  insi|ht  ^as  come  distinct,  definite,  and  adequate,  mclud- 
mom  peribct”11  ing  all  that  belongs  to  the  class-conception 
and  nothing  that  does  not,  does  our  knowledge  of  the 
objects  in  that  department  become  a matter  of  insight, 
or  of  a priori  intuition  and  affirmation.  And  upon  this 
part  of  what  we  know  of  the  objects  in  any  science, 
does  the  science  itself  depend  for  its  existence  as  a 
science. 

1067.  It  is  worthy  of  note  that  Demonstration  being 
conciusioiifrom  occupied  with  necessary  matter  exclusively, 
m“sesular  Pre'  we  may  have  a universal  conclusion  when, 


UI.]  METHODS  OF  PROOF  AND  REFUTATION. SECT.  n.  287 

as  is  usually  the  case,  the  Minor  Premise  is  Particular, 
or  rather  Individual,  including  in  fact  only  one  instance. 
Thus  in  regard  to  the  side  of  the  triangle,*  and  the 
position  of  a straight  line,f  we  have  no  hesitation  in 
including  in  our  conclusion  all  sides  of  all  possible 
triangles  and  all  possible  straight  lines,  although  in 
our  demonstration  our  attention  may  have  been  con- 
fined to  a single  case  alone.  This  results  from  the 
nature  of  the  matter,  and  is  more  obvious  in  general 
practice  than  in  the  statement  just  made,  for  then  a 
diagram  is  usually  drawn,  and  the  line,  &c.,  is  desig- 
nated as  line  AB,  or  by  some  other  such  sign. 

1068.  It  is  obvious  from  this  slight  examination 
that  Demonstration  is  not  a Formula,  but  a Demonstration 
Method  in  which  any  Formula  may  he  used  whkhTmy  fo“ 
as  bests  suits  the  taste  or  the  matter  at  our  may  be 
disposal. 

1069.  It  should  he  distinctly  observed,  however, 
that  nothing  accidental  enters  into  the  De-  No  contingent 
monstration — that  is,  nothing  except  what  into  the  scope 
was  either  contained  or  necessarily  implied  in  the  process 
in  the  class-conception  of  the  subjects  of  the  uonDemonstra' 
several  propositions.  Thus  when  we  speak  of  a tri- 
angle, all  the  matter  that  is  contained  in  the  conception 
is  “ a figure  made  by  three  straight  lines  so  meeting 
as  to  make  three  angles.”  The  Differentia  right-an- 
gled, isosceles,  equilateral,  scalene,  Ac.,  does  not  enter 
into  the  Demonstration,  concerning  triangles  merely. 
But  as  triangle  is  the  genus  which  includes  all  of  these 
species,  when  we  have  proved  the  proposition  of  the 
genus,  it  must  hold  true  of  every  included  species. 

1070.  The  Demonstration,  moreover,  holds  true  only 
of  the  reality  of  truth,  represented  by  the  Conception, 
and  not  by  any  means  or  necessarily  of  any  diagram 

* “ Any  one  side  of  a triangle  is  less  than  the  sum  of  the  two  other 
sides.” 

f “ A straight  line  let  fall  from  any  point  without  a straight  line  per- 
pendicular to  that  line  is  the  shortest  line  that  can  be  let  fall  from  the  point 
to  the  straight  line.” 


288 


LOGIC. — PAUT  II. 


[chap. 


which  we  may  draw,  or  of  any  piece  of  matter  which 
may  be  brought  into  the  form  of  a triangle.  For  not 
the  diagram  nor  the  piece  of  matter  was  the  subject  of 
our  Demonstration  ; they  serve  only  to  illustrate  and 
represent  it  at  most,  and  the  conclusion  holds  good  of 
them  only  in  proportion  as  they  conform  to  the  con- 
ception. 

1071.  An  Hypothesis,  as  we  have  seen  (827),  is  a 

Hypotheses  supposition  or  nuess  put  into  the  place  of  a 
used.  tact  or  a judgment,  m the  structure  ot  an 

argument  or  system  of  any  kind. 

• Of  the  case  in  which  hj-potheses  are  unintention- 
ally mistaken  for  facts  or  ascertained  truths,  or  of 
those  cases  in  which  they  are  'intentionally  but  fraudu- 
lently and  surreptitiously  introduced  instead  of  fact 
and  truth  we  have  nothing  here  to  say  : the  first  consti- 
tutes a fallacy  in  matter,  and  the  latter  is  a mere  trick 
of  sophistry. 

1072.  But  there  is  a legitimate  use  of  hypotheses  in 
Demonstrations.  Thus  in  Mathematics  we  have  a 
theorem  enunciated — we  suppose  cases,  for  the  sake  of 
testing  it.  We  may  suppose  the  contradictory  of  the 
theorem  and  disprove  it,  thus  proving  the  theorem. 

ah  s bin  we  may  suPPose  various  cases  to  test  the 
ties  reali°fnl  Ne-  comprehensiveness  and  adaptability  of  the 

cessary  Matter.  . x • j 1 -r  "Ii  n ** j.  i 

principle  enunciated.  In  the  first-named 
case  either  the  hypothesis  or  the  theorem  is  impossible 
and  absurd,  and  the  method  adopted  enables  us  to 
determine  what  is  absurd  and  by  consequence  which 
is  true.  In  the  last  case  the  only  limit  to  the  right  to 
make  suppositions  is  that  they  be  possible.  For  as  in 
necessary  matter  there  can  be  no  exceptions,  so  any 
rule  or  principle  must  meet  all  conceivable  cases  com- 
ing under  that  rule  or  principle.  If,  therefore,  we  can 
suppose  one  that  is  possible,  it  is  just  as  good  for  the 
sake  of  any  argument  claiming  to  be  based  on  a priori 
grounds,  as  if  instead  of  being  merely  supposed,  it  were 
actually  real.  For  in  necessary  matter  all  conceiv- 
able things  are  possible,  and  so  must  be  included 


m.J  METHODS  OF  PROOF  AND  REFUTATION. SECT.  II.  289 

within,  the  comprehensiveness  of  the  class-concep- 
tion.* 

1073.  But  in  contingent  matter  it  is  far  otherwise. 
Here  we  are  hardly  competent  to  judge  of  NotSoincon- 
the  possibility  of  what  may  become  or  may  tmgent  Matter- 
have  become  real.  And  in  moral  matter  the  danger 
of  resorting  to  hypotheses  is  still  greater. 

1074.  In  contingent  matter  we  may  use  hypotheses 
or  supposed  cases  for  the  sake  of  illustration.  Legitimate  use 
But  even  then  we  must  be  careful  that  they  contingent 
are  not  only  supposable  hut  also  possible.  Matter- 
We  never  do  and  never  can  understand  sufficiently  the 
designs  of  the  Creator  and  the  limits  to  the  possibility 
of  the  realities  of  being,  to  be  very  confident  in  our 
opinions  as  to  the  possible  and  the  impossible  in  con- 
tingent matter.  There  are  always  influences  and  prin- 
ciples at  work  of  which  we  know  but  very  little,  and 
others  of  whose  very  existence  we  know  nothing,  ex- 
cept the  constant  appearance  of  unaccountable  events 
and  facts— events  and  facts  which  in  our  ignorance  of 
these  principles  we  ascribe  to  chance — to  render  a 
resort  to  hypotheses  as  elements  in  the  construction  of 
arguments  and  sj^stems  in  all  cases  of  contingent  mat- 
ter unsafe. 

1075.  From  the  account  which  we  have  now  given 
of  Demonstration,  it  will  be  seen  that  while 

in  some  cases,  as  in  Mathematics,  Logic,  ii?l“0Method" 
Ethics,  &c.,  it  will  constitute  the  whole  of  ot  Proot 
the  Proof,  it  will  also  enter  more  or  less  extensively 
into  all  the  other  Methods  as  subordinate  parts.  For 
in  all  there  must  he  some  reliance  upon  or  reference  to 
the  force  of  the  terms,  some  analysis  and  development 
of  the  matter  necessarily  contained  or  implied  in  the 
conception  of  the  subject  of  the  Argument.  It  is  this 
part  of  an  argument  which  gives  it  much  of  what  it 
has  of  clearness  and  cogency.  If  it  does  not  give  the 

* In  fact  it  has  been  held  by  one  class  of  philosophers  that  Mathema- 
tics is  based  wholly  on  hypotheses. 

13 


290 


LOGIC. PAKT  II. 


[chap. 


argument  force,  it  makes  tlie  force  which  it  has,  felt, 
and  often  carries  conviction  where  it  would  not  other- 
wise be  produced.  I know  of  no  illustration  of  this 
remark  so  good  as  is  to  be  found  every  where  in  Web- 
ster’s Argumentative  Speeches.  And  no  mind,  so  far 
as  I have  known,  has  ever  surpassed  his  in  the  capacity 
to  see  what  was  necessarily  contained  or  implied  in 
the  conception  of  any  subject,  and  to  develope  it  with 
overwhelming  force  of  conviction. 

1076.  And  in  all  sciences  it  will  he  found  that 
before  the  facts  can  be  constructed  into  a science  at  all, 

some  fundamental  Principles  or  Axioms* 
an  sciences  a"  must  be  evolved  by  analysis  of  the  concep- 
lundamentai  tioii  of  subject-matter,  and  proved  by  De- 
monstration.  Methods  of  Investigation  may 
he  necessary  to  precede  this  step  in  order  to  give  us 
adecpiate  conceptions  of  the  subject-matter  from  which 
to  evolve  and  demonstrate  the  fundamental  principles. 
But  these  principles  themselves  must  be  demonstrated 
a priori  before  the  science  can  receive  any  permanent 
or  satisfactory  form. 

SECTION  III. 

Of  Deduction. 

1077.  By  Deduction  we  mean  the  Method  or  Pro- 
peduction.  cess  of  proving  a Proposition  with  a less 
comprehensive  subject,  as  a Conclusion  from  one  with 
a more  comprehensive  subject,  by  the  subsumption  of 
the  less  under  the  more  comprehensive — the  Predicates 
of  both  being  common.  Thus  in  Barbara  : 

M is  P, 

S is  M, 

.-.  S is  P. 

* The  difference  between  an  Axiom  and  a Maxim  is,  that  the  latter  is 
a general  truth  obtained  by  classification  and  induction  to  a maximum 
genus ; whereas  an  Axiom  is  a necessary  truth,  and  may  be  either  intuitive 
or  obtained  by  demonstration  from  the  necessary  matter  of  the  class-con- 
ception of  the  subject. 


HI.]  METHODS  OF  PROOF  AND  REFUTATION. SECT.  m.  291 

Here  S is-  subsumed  as  a class  under  M in  the 
Minor  Premise,  whence  it  follows  that  M is  the  more 
comprehensive  Sphere  of  the  two,  and  that  P is  predi- 
cable of  S if  it  may  he  predicated  of  M. 

1078.  Deduction  forms  a large  part  in  the  develop- 
ment and  completion  of  any  science.  A few  The  Sphere  of 
leading  principles  are  ascertained  from  oh-  Deduction- 
servation  and  experience,  and  from  them  deduction  is 
made  to  particular  facts  with  much  more  ease  and 
certainty  even,  in  most  cases  than  an  observation  of  the 
fact  itself  could  be  made.  And  in  many  cases,  as  in 
Physiology,  the  fact  is  beyond  the  reach  of  any  ob- 
servation ; or  in  others,  as  in  Astronomy  for  instance, 
it  will  not  come  round  in  centuries  perhaps.  Thus  the 
details  of  any  science  will  be  made  out  to  a consider- 
able extent  by  deduction  from  its  general  principles. 

1079.  In  the  practical  application  of  sciences  the 
Method  is  always  deductive.  Even  those  Thg  th  d 
books  which  are  written  with  the  most  espe  - always  deduc- 
cial  reterence  to  application  to  practice,  never  plication  0f  sol- 
do and  never  can  mention  and  enumerate  all  ence' 

the  individual  cases.  The  most  they  can  do  is  to 
specify  classes  of  cases,  and  the  more  nearly  in  their 
enumeration  of  classes — that  is,  in  their  division  and 
classification — they  approach  to  the  Infima  Species , 
the  more  practical  do  they  become  in  the  ordinary 
sense  of  the  word. 

1080.  In  that  case  the  Infima  Species  is  the  Middle 
Term,  the  particular  individual  case  to  which  the  ap- 
plication is  to  be  made  is  the  Minor  Term,  and  the 
other  term,  whether  Subject  or  Predicate,  which  enters 
into  the  “ Precept,”  as  it  is  called,  with  the  Infima 
Species  as  the  Middle  Term,  is  the  Major  Premise. 

1081.  Thus  the  physician  examining  a patient 
decides  the  case  to  be  intermittent  fever.  niustrati0n  in 
His  science  has  taught  him  that  quinine  is  pharmacy- 
required  in  intermittent  fevers.  Accordingly  he  pre- 
scribes quinine.  His  reasoning,  stated  at  length,  is  as 
follows  : 


292 


LOGIC. — PART  II. 


[CHAP. 


Intermittent  fevers  require  quiriine  ; 

This  case  is  an  intermittent  fever  : 

.•.  This  case  requires  quinine. 

1082.  It  will  be  seen  at  once  that  this  is  precisely 
the  form  in  which  the  principles  of  science  are  applied 
to  useful  purposes. 

1083.  In  the  same  way  established  principles  and 
in  Astronomy,  laws  are  applied  to  new  cases.  For  exam- 
ple, in  Astronomy  the  laws  of  motion,  the  relation  of 
distance  to  time  in  the  periodic  revolutions  of  planets, 
comets,  &c.,  are  so  well  known  that  the  moment  a new 
one  is  discerned,  the  astronomer  proceeds  by  way  of 
demonstration  to  determine  from  those  elements  of  its 
sphere  nearly  all  that  can  be  known  about  it,  without 
waiting  for  the  much  slower  and  more  tedious  process 
of  observing  these  revolutions,  as  they  occur  in  the 
course  of  centuries  of  our  years. 

1084.  It  will  have  been  observed  that  one  leading 
i AomeScimofl  °^j e°t  i11  Methods  of  Investigation  is  to  de- 
.ieductive  ““as  temiine  definitely  and  adequately  the  class- 
more  penect.  conceptions  which  are  based  upon  the  nature 
of  things  in  the  reality  of  being.  It  has  been  remarked* 
that  just  in  proportion  as  any  science  progresses  from 
its  inception  and  the  first  rude  accumulation  of  ele- 
mentary facts,  does  it  become  more  and  more  deductive 
and  even  demonstrative  in  its  Methods.  Our  class- 
conceptions  of  its  subject-matter  by  this  means  become 
more  distinct,  definite,  and  adequate — more  conformed 
to  the  constitutive  Idea  of  the  classes,  more  compre- 
hensive of  individuals  and  of  phenomena  — and  our 
confidence  in  the  results  and  teachings  of  that  science 
become  proportionally  great. 

* Mill’s  Logic , Book  II.  Chap.  IV.  § 6. — See  also  Devey,  Book  V. 
Chap.  I.  §.  5. 


m.]  METHODS  OF  PROOF  AND  REFUTATION. SECT.  IV.  293 


SECTION  IV. 

Of  the  Argument  from  Authority. 

1085.  There  are  many  Propositions,  which  from 
their  relating  to  subjects  above  our  compre-  Authority  of 
hension,  or  from  their  being  beyond  the  Revelatlon- 
reach  of  our  observation,  and  differing  so  far  from  what 
we  can  observe  and  know  in  this  state  of  being  that 
Analogy  fails  to  be  a safe  guide,  can  be  proved  only 
by  an  appeal  to  the  Authority  of  God  in  the  Revelation 
which  Tie  has  been  pleased  to  make. 

1086.  Then  we  have  also  another  class  of  Propo- 
sitions in  which  stat  pro  ratione  voluntas,  Authority  of 
where  the  will  of  some  Authority  so  deter-  Governance- 
mining,  is  the  ground  and  the  only  ground  on  which 
we  are  obliged  to  receive  them  as  true,  because  they 
have  been  so  declared  by  a competent  authority. 

1087.  Of  this  kind  are  the  laws  of  a State,  whether 
enactments  of  the  legislature,  or  decisions  of  the  courts, 
for  all  citizens  ; the  laws,  canons,  rubrics,  &c.,  of  a 
Church  for  all  its  members  : the  constitu- 

tions,  rules,  and  by-laws  oi  any  voluntary  only  limited  ob- 
society  or  corporation  tor  economical,  social, 
moral,  political,  philanthropic  or  religious  purposes, 
upon  the  members  of  those  societies  or  corporations  as 
members  and  during  their  membership. 

1088.  Propositions  of  the  kind  now  under  consider- 
ation are  authority,  and  therefore  to  be  received  as  true 
only  in  relation  to  the  particular  things  which  come 
under  the  jurisdiction  of  the  authority,  and  for  those 
persons  over  whom  that  authority  justly  extends. 
Thus  Revelation  is  final  to  all  the  creatures  of  God 
to  whom  it  is  made ; the  authority  of  the  state  to  all 
citizens  and  subjects;  that  of  a voluntary  society  to 
those  only  who  voluntarily  belong  to  the  society. 

1089.  There  are  some  spheres  in  which  by  the  very 
nature  of  the  case  this  Means  of  Proof  is  made  neces- 


294 


LOGIC. — PART  II. 


[CHAP. 


sary,  and  is  the  only  one  that  is  proper.  In  Statute 
Luav  and  Theology,  for  instance,  the  dicta 
only1  e'roui]d°in  of  the  proper  Authority  must  be  an  end  to 

some  cases.  . 1 x ° 

controversy.  Any  arguments  on  general 
grounds,  as  to  what  ought  to  he  true , can  do  nothing 
more  at  most  than  to  create  a presumption  in  favor  of 
any  doctrine. 

1090.  Besides  the  foregoing,  the  common  sense  or 
consent  of  mankind,  as  well  as  the  admissions  of  those 

against  whom  we  are  arguing,  become  first 
and  “common  principles  of  the  nature  of  authority  within 
certain  limits,  and  to  certain  persons  the 
argument  from  the  admissions  of  parties  ex . concessis , is 
scarcely  any  thing  more  than  an  argumentum  ad  homi- 
nem , and  for  that  I will  refer  the  reader  to  Sec.  XI.  of 
this  Chapter  below. 

1091.  But  the  common  opinion  of  men  is  an  Au- 
thority or  first  principle,  on  which  a large  part  of  our 

Extent  of  ciost  important  deductions  are  based,  espe- 
mo?!1  a°a  pmi  cially  in  practical  matters,  and  among  those 
dole.  whose  minds  have  never  been  trained  to 

look  into  the  philosophical  grounds  of  their  actions. 

These  are  commonly  called  Arguments  from  Corn- 
common  sense  111011  Sense,  sensus  communis  omnibus , and 
fuesVinridmerent  their  value  has  been  very  variously  esti- 

Spheres.  mated. 

1092.  In  matters  of  Religion,  if  man  is  to  he 
Religion.  regarded  as  a fallen  and  depraved  being,  it 
is  to  he  distrusted  and  scanned  very  closely.  In  fact 
it  can  never  be  used  except  as  confirmatory  of  the 
Argument  from  authority,  or  as  serving  the  rhetorical 
purpose  of  removing  a prejudice  or  supposed  antece- 
dent improbability.  But  if  man  is  not  fallen  or  de- 
praved, his  common  sense  must  be  as  infallible  an 
indication  of  the  law  and  will  of  God  (vox  joojnili  vox 
Dei ),  as  the  facts  and  changes  of  the  physical  world 
are  of  Iiis  laws  and  will  in  relation  to  matter. 

1093.  In  Polity  and  Ethics  the  common  sense  of 
man  is  of  more  value  ; for  they  relate  to  matters  that 


in.]  METHODS  OF  PROOF  AND  REFUTATION. SECT.  IV.  295 

are  more  comprehensible,  and  which  have  of  necessity 
been  not  only  subjects  of  reflection,  hut  also  In  PoUty  and 
and  moreover  they  have  been  tested  by  the  Ethics- 
experience  of  all  and  in  all  ages.  What  has  been  thus 
found  to  he  best  and  true,  is  most  likely  to  stand  the 
trial  to  which  it  can  be  brought.  The  latter  schools 
of  philosophy  have  professedly  regarded  this  common 
sense  as  of  great  value  as  a standard  of  truth. 

1094.  In  the  Natural  Sciences  it  has  been  found  to 
he  an  unsafe  guide.  It  always  depends  upon  tn  the  Natural 
the  appearances  of  things,  while  in  many  Sciences- 
cases  the  reality  lies  much  deeper  and  is  often  very 
unlike  the  appearance.  The  contrast  between  the  com- 
mon belief  in  regard  to  the  motion  of  the  Sun  and  the 
Earth  is  familiar  to  all,  and  a case  in  point. 

1095.  But  in  matters  which  depend  upon  a priori 
conceptions  or  upon  facts,  the  appeal  to  com-  In  the  Pure 
mon  opinion  is  out  of  place.  By  authority,  Sciences- 
however,  in  this  connection,  I do  not  mean  testimony 
to  the  reality  of  facts.  Such  testimony  we  must  use 
and  depend  upon.  But  testimony  to  a fact  Distincti0n  be 
is  one  thing,  and  opinion  or  inference  from 

the  fact  is  quite  another.  And  the  differ-  mony- 
ence  between  them  is  one  of  the  things  which  it  is  most 
important  to  notice.  Testimony  is  the  means  by  which 
we  know  what  are  the  Principles  which  have  been 
established  by  Authority.  Thus  in  Religion,  God  him- 
self is  the  Authority ; and  the  Scriptures  are  the  Testi- 
mony which  make  known  to  us  what  has  emanated 
from  that  Authority.  In  Law,  the  State  is  the  Author- 
ity ; and  the  statute-books  and  the  decisions  of  the 
Courts  are  the  Testimony  from  which  we  learn  what 
are  the  laws  established  by  that  Authority. 

1096.  Hence,  although  we  may  use  testimony  in 
the  Natural  Sciences,  in  History,  &c.,  Au-  Legitimate  use 
thority,  strictly  speaking,  we  do  not  use.  ot  Test‘m°“y- 
We  use  testimony  as  a means  of  ascertaining  facts, 
whether  they  be  the  facts  which  any  Authority  has 
made  such,  as  when  a State  enacts  a law,  that  enact- 


296 


LOGIC. — PART  II. 


[chap. 


ment  is  a fact ; or  whether  they  are  the  facts  evolved 
in  the  history  of  man  and  the  world,  or  finally  the  facts 
of  Nature. 

1097.  Yet  even  Testimony  is  often  called  Author- 
Testimony  of-  ity — an  authority  for  believing  the  Tacts  to 

thority.  which  it  bears  witness  only.  We  speak  of 
believing  a fact  in  Roman  history  on  the  authority  of 
Livy  or  of  Tacitus,  when  in  strictness  of  language  we 
in  what  sense,  mean  the  testimony  of  those  writers.  This 
distinction  between  Authority  and  Testimony  is  indis- 
pensable to  a right  apprehension  of  Methods  of  Investi- 
gation and  Argument  in  which  they  are  used. 

1098.  Testimony  can  prove  facts  only,  and  a law  or 
an  opinion  only  as  the  facts  themselves  prove  the 

in  what  way  opinion.  Testimony  may  prove  the  acts  and 
Jrovema°nnyopTnn  words  of  our  Lord,  as  recorded  in  the  Holy 
ion  or  jaw.  Scriptures.  But  these  acts  and  words,  as 
facts , must  prove  the  Revelation,  and  that  that  which 
is  given  as  a Revelation  of  the  Will  of  Grod  is  really 
His  will.  Testimony  can  prove  the  enactment  of  a 
law,  or  the  issuing  a command — but  the  enactment 
itself,  and  the  giving  of  the  command,  as  facts  must 
prove,  if  it  is  proved  at  all,  that  the  law  enacted 
and  the  command  given  are  laws  and  commands  of 
Authority. 

1099.  Hence  in  Mathematics  Testimony  is  never 
Testimony  used  as  a means  of  Teaching  or  of  Proof. 

o'fhbeHerfround  All  must  rest  on  the  personal  intuition  of  the 
learner.  In  the  Natural  Sciences  we  have  to  depend 
upon  Testimony  for  a large  part  of  our  facts.  But  the 
facts  speak  for  themselves.  Testimony  cannot  even 
prove  an  opinion , but  only  the  fact  that  such  and  such 
an  one  held  it  as  an  opinion.  It  does  not  prove  the 
opinion  to  he  true  ; and  all  that  can  be  gained  by  the 
opinion  of  others  in  the  fields  of  scientific  inquiry,  is  at 
most  a probable  ground  of  action , when  we  must  act 
and  can  have  nothing  l>ettcr  to  act  upon. 

1100.  Thus  a physician,  in  a critical  case,  may  act 
And  of  Action,  upon  a mere  opinion  of  a distinguished 


in.]  METHODS  OF  PROOF  AND  REFUTATION. SECT.  IV.  297 


physician,  provided  there  is  no  prescription  for  it 
which  experience  has  satisfactorily  proved,  and  where, 
if  he  does  not  act  at  all,  only  the  worst  of  consequences 
can  ensue. 

1101.  In  all  appeals  to  Authority,  and  to  Testimony 
also,  howsoever  and  wheresoever  expressed,  Necessity  f0r 
the  true  meaning  of  the  words  in  which  it  is  inn7hTeuseioof 
expressed  is  of  material  importance,  and  of  Authonly- 
course  one  of  the  first  things  to  be  obtained.  Language 
itself  is  but  an  imperfect  instrument  for  the  expression 
of  thought,  and  often  it  is  used  without  clearness  in  the 
mind  of  him  who  uses  it,  and  without  any  successful 
effort  to  make  it  as  adequate  to  the  expression  of  the 
thought  as  its  capabilities  would  allow. 

1102.  The  process  by  which  we  evolve  a man’s 
thoughts  from  his  words,  is  called  Interpre- 
tation or  Hermeneutics.  Something  of  inter-  orIn 5™“ 
pretation  is  always  necessary  when  we  read. 

But  when  such  words  are  used  as  we  are  familiar  with, 
and  the  clear  thought  is  clearly  expressed  in  familiar 
phrase,  the  process  of  interpretation  is  performed  so 
quickly  and  so  easily,  that  we  are  wholly  unconscious 
of  it.  It  is  only  when  it  becomes  difficult,  and  takes 
time,  and  causes  delay  and  doubt,  that  we  become 
conscious  of  the  effort,  and  feel  the  need  of  rules  and 
principles  to  guide  us. 

A few  of  these  leading  and  most  important  princi- 
ples we  will  now  briefly  specify. 

1103.  (1)  In  the  first  place,  wherever  there  is  one 

plain  and  obvious  meaning  to  a passage,  that  takendsi™utheh- 
is  to  be  adopted.  fnbgvious  mta"~ 

Seldom,  indeed,  will  it  be  expedient  or  allowable  to 
go  behind  the  text  itself  to  any  evidence  or  indications 
of  what  the  author  may  have  intended  to  say,  provided 
his  language  is  clear  and  appears  to  have  been  used  by 
one  who  knew  how  to  express  whatever  thought  he 
may  have  intended  to  communicate.  The  choice  of 
words  and  expressions  was  with  him,  and  he  must  be 
responsible  for  what  he  has  clearly  and  plainly  said. 

13* 


298 


LOGIC. PART  n. 


[chap. 


1104.  (2)  But  secondly,  where  language  is  ambi- 
Ambiguous  lan-  guous,  or  the  meaning  of  a passage  is  doubt- 
terpretcd0"  ful,  we  are  to  interpret  in  accordance  with 
truth  and  right  sentiment  if  possible. 

This  rule  is  charitable  enough,  and  may  sometimes 
give  one  more  than  his  due.  But  it  is  better  to  do  so 
than  otherwise.  Let  the  error,  if  there  be  one,  be  put 
down  to  the  account  of  charity. 

1105.  (3)  Thirdly,  we  must  take  heed  to  the  usus 
quendi.USUS  '0'  loquendi  / 

(a)  Of  the  author  himself. 

(b)  Of  the  sect  or  people  to  which  he  belongs. 

There  is  scarcely  a writer  or  speaker  who  has  not 

some  peculiarities  in  style,  and  in  the  use  of  some  of 
the  words  which  will  occur  in  the  course  of  his  writings 
or  speeches.  The  exact  meaning  of  such  words,  as 
used  by  any  man,  is  best  obtained  from  a study  of  his 
own  writings  ; or  secondly,  in  case  there  are  none,  in 
those  of  the  sect  or  school  to  which  he  belongs.  Thus 
the  word  “ Idea  ” means  one  thing,  in  Plato’s  use  of 
it,  another  in  Mr.  Locke’s,  and  still  another  in  the  writ- 
ings of  some  modern  philosophers,  as  Kant  and  Cousin. 
If,  therefore,  we  should  undertake  to  read  the  writings 
of  any  one  of  these  authors,  with  the  sense  which  the 
other  attaches  to  the  word  whenever  it  occurs,  we  not 
only  should  fail  to  find  our  author  very  clear  and  intelli- 
gible, but  we  should  deduce  from  his  statements  conclu- 
sions which  his  words,  when  understood  as  he  intended 
them , would  not  justify.  It  would  be  easy  to  accumu- 
late a long  list  of  words,  illustrating  this  point,  but  we 
have  not  room. 

1106.  (4)  The  fourth  rule  is,  that  technical  terms 
Technical  Terms,  must  be  explained  by  the  science  to  which 
their  use  belongs. 

Every  science  has,  and  of  necessity  must  have  some 
terms  to  which  those  who  are  proficient  in  that  science 
will  attach  a meaning,  somewhat  different  from  that 
which  it  has  among  those  who  are  unacquainted  with 
its  scientific  use.  The  word  “ switch,”  as  used  by 


in.]  METHODS  OF  PROOF  AND  REFUTATION. SECT.  IV.  299 

boys  at  their  plays,  and  by  a railroad  manager,  has 
two  entirely  distinct  senses.  In  fact  no  one  can  read 
any  treatise  on  a scientific  subject  with  which  he  is 
unacquainted  without  finding  new  words,  and  old  words 
used  with  new  significations.  Lexicographers,  in  pre- 
paring their  Dictionaries,  derive  their  definitions  from 
the  sources  now  indicated,  or  at  least  should  do  so. 
But  in  no  case  can  a Dictionary  give  all  the  technical 
words  with  all  their  meanings.  Let  any  one,  for  in- 
stance, attempt  to  find  in  any  Dictionary  a definition 
of  the  terms  used  by  sailors  at  sea,  by  printers  in  the 
ju’inting-office,  to  say  nothing  of  the  technicalities  of 
Law,  Medicine,  and  Theology,  and  he  will  see  the 
necessity  and  reasonableness  of  the  rule  of  interpreta- 
tion now  laid  down. 

1107.  (5)  All  language  used  in  deeds,  wills,  and 
other  documents,  conveying  property  from 

one  to  another,  are  to  be  interpreted  in  favor  giving  ana  con- 
of  the  grantor,  if  there  is  any  of  ambiguity. 

The  obvious  reason  for  this,  is  that  the  right  of 
property  requires  that  no  one  should  be  presumed  to 
have  intended  to  give  away  any  more  than  he  ex- 
pressed his  intention  to  give. 

1108.  But  to  this  there  are  several  modifications  ; 
and  the  first  is  in  conveying  away  any  obj ect,  Modifications 
we  convey  with  it  whatever  is  inseparable  totherule- 
from  it,  even  though  it  be  not  mentioned  ; and  secondly, 
as  a grant  is  seldom  if  ever  made  except  for  a consider- 
ation of  something  in  return,  the  amount  of  this  con- 
sideration may  sometimes  be  taken  into  account  to 
determine  the  true  sense  of  the  grant. 

1109.  (6)  Oaths  are  always  to  be  understood  (in 

sensu  iinrponentis ),  in  the  sense  of  the  au-  oaths, 

thority  which  imposes  the  oath. 

Oaths  are  given  to  secure  the  fidelity  and  truthful- 
ness of  those  on  whom  they  are  imposed.  But  if  those 
who  receive  the  oaths  may  take  advantage  of  any  ob- 
scurity or  ambiguity  which  may  exist  in  the  language 
of  the  oath  itself,  or  which  by  ingenuity  and  prejudice 


300 


LOGIC. PART  n. 


[CHAP. 


persons  interested  can  cause  to  exist,  the  obligations 
of  an  oath  and  the  very  purposes  for  which  they  are 
imposed  will  be  at  an  end.  One  has  a right  to  know, 
before  taking  an  oath,  what  it  means  and  what  it  is 
designed  to  impose  upon  him.  And  although  he 
would  be  justified  in  some  cases  in  refusing  the  oath 
and  submitting  to  the  consequences,  yet  in  no  case 
would  one  be  justified  in  taking  the  oath  and  then  per- 
juring himself,  under  the  plea  that  the  oath  is  suscep- 
tible of  another  construction,  than  that  designed  by 
the  authority  imposing  it,  or  that  he  chose  to  put  an- 
other construction  upon  it. 

1110.  (7)  All  laws,  edicts,  &c.,  restraining  personal 
Laws,  Edicts,  liberty  and  the  right  of  private  judgment, 

restraining  lib-  , />  J ° , 7 

crty.  are  to  be  interpreted  as  lavorabiy  as  possible 

to  those  who  are  thus  restrained. 

All  law  and  authority  is  of  necessity  and  essentially 
a restraint  upon  the  personal  liberty  of  those  who  are 
subject  to  the  law  or  authority.  We  seldom  speak  of 
it  in  this  light,  however,  except  where  the  restraint 
becomes  greater  than  there  is  any  good  reason  for. 
But  as  such  restraints  should  be  as  little  as  the  cause 
of  order  and  morality  will  allow,  we  are  to  interpret 
all  laws  which  go  beyond  those  requirements  in  favor 
of  the  subject,  and  give  him  the  benefit  of  any  ambi- 
guity that  there  may  be  in  the  language  in  which  the 
laws  are  expressed. 

1111.  (8)  Commissions  and  other  documents  con- 
commissions  ferring  authority  or  privilege,  are  to  be 

privilege.  regarded,  as  iLxclusives  ( expressio  unites, 
exclusio  alterius).  This  is  substantially  the  same  as 
the  fifth  rule  above,  in  a different  application.  No 
one  is  presumed  to  have  any  authority  over  another, 
or  special  privileges  and  exemptions.  If  he  has  them 
there  must  be  proof  of  it,  and  the  mention  of  one  or 
more  in  the  words  that  confer  the  authority  or  privilege, 
leaves  the  others  in  possession  of  no  more  than  they 
would  have  had  if  no  such  document  had  been  issued. 
The  commission  of-  one  man  in  a company  does  not 


m.]  METHODS  OF  PROOF  AND  REFUTATION. SECT.  IV.  301 

constitute  all  the  privates  captains.  Nor  does  the 
appointment  of  one  man  to  be  a justice  of  the  peace 
make  the  whole  neighborhood  to  he  esquires. 

1112.  (9)  When  the  quantity  of  a proposition  is 
doubtful  we  are  to  take  it  at  its  least  value,  The  Quantity 
unless  the  conclusions  of  the  argument,  or  °faPr0p0i‘tl0n- 
the  truth  of  the  statement  require  otherwise. 

Thus  in  Wayland’s  Political  Economy  occurs  the 
remark,  which  is  universal  in  its  form,  “ All  men  are  not 
merchants .”  But  truth  requires  that  it  be  considered  as 
particular  negative — that  is,  “ Some  men  are  not  mer- 
chants.” And  again  ; from  the  connection  in  which  it 
occurs,  it  appears  to  have  been  designed  as  a contra- 
dictory of  a supposed  preceding  universal  affirmation, 
“ All  men  are  merchants.”  Again,  the  following  oc- 
curs in  a work  before  me,  “ Abstinence  from  eating 
flesh  had  reference  to  the  divine  institution  of  sacri- 
fice ; ” the  author’s  argument,  as  well  as  the  ordinary 
principles  of  interpretation,  require  that  the  proposition 
should  be  regarded  as  universal.  But  the  truth  of  the 
proposition  would  in  that  case  be  a matter  of  doubt  at 
least,  and  most  likely  the  proposition  would  be  false  if 
taken  universally.  But  if  the  proposition  had  occurred 
where  no  use  was  made  of  it,  requiring  it  to  be  regard- 
ed as  a universal  proposition,  it  would  have  passed 
without  notice  as  a statement  generally  true,  perhaps, 
but  yet  only  the  expression  of  a particular  judgment, 
“ Abstinence  ” being  regarded  as  not  a distributed 
term ; the  abstract  term  being  used  for  the  concrete 
plural. 

1113.  (10)  Parables  and  metaphors  are  to  be  con- 

strued with  special  reference  to  the  design  Parabies  and 
for  which  they  were  used.  Metaphors. 

Parables,  metaphors,  fables,  and  all  of  that  kind  of 
illustrations,  are.  based  upon  analogy  and  not  identity 
of  cases.  But  in  all  analogies  there  are  points  of 
diversity,  and  the  case  upon  which  the  parable  is  based 
is  assumed  to  be  identical  only  in  the  point  to  be  illus- 
trated by  it.  In  that  point  there  must  be  identity,  else 


302 


LOGIC. — PAHT  n. 


[chap. 


tlie  illustration  fails  ; beyond  that  point  there  must  be 
some  diversity.  These  points  must  not  be  brought  into 
the  illustration,  nor  may  its  force  and  appropriateness 
be  objected  to  on  their  account. 

1114.  In  the  Parable  of  the  Rich  Man  and  Laza- 
rus (Luke  xvi.),  for  instance,  the  main  design,  undoubt- 
edly, was  to  show  the  impossibility  of  changing  one’s 
doom  by  repentance  after  death.  And  it  would  be 
unsafe  and  unwise  to  attempt  to  infer  any  thing  further 
frgm  it  concerning  the  condition  of  man  in  the  future 
state.  We  can  hardly  go  so  far  with  safety,  (I  think,) 
as  to  infer  from  it  that  the  two  classes  of  persons  repre- 
sented by  Lazarus  and  the  Rich  Man,  are  in  a condi- 
tion to  hold  conversation  with  each  other,  or  with  those 
of  the  other  class  at  all. 

1115.  (11)  Mere  obiter  dicta  are  never  to  be  re- 

obiter  dicta,  garded  as  of  equal  authority  with  the  as- 

sertions made  to  the  point  directly  before  the  mind. 

In  nearly  all  discourse  and  reasoning  there  is  a 
leading  object,  to  which  the  attention  is  especially 
directed.  The  assertions  bearing  directly  on  that  point 
are  always  to  be  regarded  as  the  most  mature  and 
carefully  guarded  opinions  of  the  author.  But  there 
are  almost  always  expressions  dropped  by  the  way, 
called  obiter  dicta , on  incidental  and  collateral  matters, 
to  which  the  attention  is  not  directed  with  so  much 
energy  as  to  the  main  point,  and  consequently  these 
obiter  dicta  are  less  valuable  as  expressions  of  opinion 
or  authority,  than  those  to  which  the  attention  is  mainly 
directed. 

1116.  The  science  of  Interpretation  is  a compre- 
speciai  Rules  hensive  one,  and  cannot  be  fully  treated  in 
departmerftl ery  this  place.  And  as  in  each  special  depart- 
ment of  inquiry,  Avhere  we  have  to  depend  upon  Testi- 
mony and  Authority,  some  special  rules  and ' cautions 
are  found  necessary,  I have  aimed  above  to  give  only 
such  general  rules  as  seemed  necessary  to  my  present 
purpose,  and  of  the  most  extensive  application. 


m.]  METHODS  OF  PROOF  AND  REFUTATION. SECT.  Y.  303 


SECTION  V. 

Of  the  Appeal  to  Facts. 

1117.  The  Appeal  to  Facts,  as  a Method  of  Argu- 
ment, is  in  some  respects  the  converse  of  the  AppeaI  t0 
foregoing  Methods.  We  reason  from  Facts  Facts- 

to  Principles  rather  than  from  Principles  to  Facts. 

1118.  These  Facts  may  he  introduced  by  way  of 
Induction,  Analogy,  Example,  or  as  Contra-  Facts  how  in. 
ries,  Exceptions,*  Circumstances,  Cause  or  troduced- 
Effect.  But  in  all  cases  they  require  the  force  of  Prin- 
ciples lying  deeper  than  the  facts  themselves,  in  order 
to  render  their  argumentative  force  of  any  value. 

1119.  I have  already  in  the  last  Chapter  (Section 
VII.)  said  concerning  reasoning  from  Cause  Cause  and  Ef. 
to  Effect — that  is,  concerning  the  appeal  to  fect- 
Facts  as  Causes  or  Effects,  all  that  I shall  deem  it 
advisable  to  say  in  the  present  Treatise.  I will,  there- 
fore, proceed  at  once  to  consider  the  general  Principles 
involved,  and  the  Methods  of  proceeding  in  reasoning 
from  Facts  in  the  various  other  conceptions  of  them. 

1120.  An  important  distinction  is  made  between  a 
law  and  a general  fact.  Thus  it  is  a general  General  Facts 
fact,  proved  by  Induction,  that  “ all  Canidse  and  Laws- 
are  carnivorous  ; ” — “ all  bodies  gravitate  towards  the 
Earth.”  But  that  which  lies  under  this  general  fact 
and  determines  the  manner  in  which  the  Cause  shall 
act,  is  called  the  law.  Hence  the  law  of  gravitation 
is  that  which  accounts  for  the  general  facts  of  gravity. 
It  is  the  law  which  produces,  or  rather  guides  the 
cause  in  producing  the  general  fact  of  a carnivorous 
habit  of  life  in  animals,  constituted  by  their  Creator 


* For  facts  introduced  by  way  of  Exceptions,  see  Sec.  IX.  below. 
Since  they  always  presuppose  that  to  which  they  are  exceptions,  I have 
chosen  to  consider  them  as  means  of  disproof ; that  is,  disproving  the  uni- 
versality of  that  rule  in  view  of  which  alone  they  can  be  regarded  as  ex- 
ceptions. 


304 


LOGIC. PART  II. 


[chap 


for  that  habit  of  life.  Hence  the  law  always  implies 
the  fact  and  the  fact  the  law,  and  the  two  are  often 
confounded. 

1121.  We  place  but  very  little  confidence,  how- 

ever, in  any  mere  induction  of  facts,  unless  we  can  go 
induction  must  a little  farther.  The  Formula  of  Induction 
mere^cfassffictu  itself,  as  will  be  seen  (569),  is  an  undistri- 
tlon-  bated  Middle,  and  becomes  valid  at  all  only 

by  a sort  of  transfer  of  the  matter  over  into  the  domain 
of  necessary  matter. 

1122.  This  we  accomplish  by  means  of  principles, 
logically  antecedent  to  all  induction,  and  lying  deeper 

how  accom-  in  the  subj ect-matter  than  Induction  itself 
piished.  can  i-eacP.  By  this  means  we  can  extend 
our  predication  from  what  is  and  has  been  to  what 
will  be.  We  pass  from  the  general  fact  to  the  law.* 

The  first  of  these  Principles  which  we  shall  con- 
sider is  the  Uniformity  of  Nature — the  second  is  that 
of  Final  Causes. 

1123.  We  use  the  word  “Nature”  \_N~atura,  from 
■Nature "in  nascor],  as  a collective  term,  including  all 

used.  senoe  those  realities  of  being  in  the  external  world, 
whose  existence  is  contingent,  and  which  are  not  the 
product  of  human  agency  as  their  Efficient  Cause. 
Thus  a blow  with  the  hand  would  not  be  a fact  in 
Nature,  since  it  proceeds  from  the  will  of  man  as  its 

* We  have  given  above,  p.  249  n.,  Aristotle’s  definition  of  Induction, 
Top.  B.  I.  Cap.  XII.  In  the  Prior  Analytics,  Book  II.  Cap.  XXII.  Aris- 
totle speaks  of  Induction  as  a means  of  proving  one  extreme  through  the 
other,  i.  e.  to  prove  the  Major  Term  of  the  Middle , by  means  of  the  Minor. 
Thus  he  gives  for  example  : 

Men,  horses,  and  mules  are  long  lived  ; 

Men,  horses,  and  mules  are  void  of  bile. 

If  then,  says  he,  (men,  horses,  and  mules)  and  (long-livers)  may  be 
converted  “ without  excluding  the  Middle,”— that  is,  if  (long-lived)  is  not 
a more  comprehensive  sphere  than  (men,  horses,  and  mules),  we  may  have 
the  conclusion  : 

All  animals  void  of  bile  are  long-lived  ; 

But  this  is  the  very  difficulty ; the  Major  Premise  can  never  be  con- 
verted in  that  way.  The  Predicate  is  always  comprehensive  of  more  than 
the  inducted  particulars,  and  it  is  precisely  this  peculiarity  of  induction  that 
we  wish  to  account  for  and  justify. 


III.]  METHODS  OF  PROOF  AND  REFUTATION. SECT.  Y.  305 


Efficient  Cause.  But  the  growth  of  a blade  of  com 
would  he  a fact  in  Nature,  although  the  growth  might 
depend  upon  the  fact  that  man  had  planted  it,  or  still 
keeps  the  soil  in  a condition  to  continue  its  growth 
towards  maturity.  In  this  case  man  is  not  the  Efficient 
hut  only  the  Occasional  Cause. 

1124.  By  the  Uniformity  of  Nature  we  mean  what 
may  be  stated  generally  as  the  fact,  that  the 

J 0 . 17  i j i i What  is  meant 

same  causes  acting  under  the  same  laws,  by  y umfomu- 
and  cwieris paribus — (that  is,  all  the  modify-  tJ' 
ing  circumstances  being  the  same,)  will  produce  the 
same  effects.* 

1125.  But  let  us  try  to  get  a little  more  definite 
idea  of  this  uniformity,  and  the  grounds  upon  which  it 
rests. 

It  is,  doubtless,  first  suggested  by  the  facts  in  the 
external  world.  Thus,  for  instance,  a tree  ^ o 
always  produces  leaves  and  fruit  of  the  same  uniformity  how 
kind.  So,  too,  with  the  offspring  of  animals.  f‘rst  ° taa,e  ' 
Each  new  individual  is  not  the  germ  of  a new  class  or 
species.  Nor  does  it  even  belong  to  a species  different 
from  that  from  which  it  derived  its  origin.  In  short 
the  objects  of  nature  at  once  suggest  the  classifications, 
by  means  of  Essentia  and  Differentia,  which  have  al- 
ready been  spoken  of  as  so  advantageous  to  science. 

* Mr.  Mill  thinks  (besides  expressing  some  doubts  about  the  Uni- 
formity of  Nature)  that  what  we  know  or  believe  of  it  we  have  learned 
from  experience.  In  a certain  sense  this  is  true.  And  using  words  still 
in  the  same  sense  all  that  we  ever  know  is  learned  from  experience.  But 
then  we  may  easily  get  to  be  wiser  than  our  teacher.  We  learn  from  ex- 
perience a great  deal  more  than  there  is  in  experience.  Experience  is  con- 
fined to  the  past,  and  generalizations  upon  its  facts  can  give  us  only  what  has 
been.  But  by  induction  from  the  facts  of  experience  we  infer  what  is  to  be 
in  the  future,  and  every  where  in  the  reality  of  being  constituted  like  that 
in  which  we  are  placed.  From  mere  uniformity  we  do  not  expect  its  con- 
tinuance, as  Mr.  Mill  has  indirectly  shown.  From  the  fact  that  the  first 
five  or  six  of  the  Presidents  of  the  United  States  retired  from  office  at  the 
age  of  sixty-six,  the  people  of  the  country  formed  no  expectation  whatever 
that  such  would  continue  for  ever  to  be  the  uniform  fact  with  regard  to  the 
age  of  the  retiring  Presidents.  Hence  it  is  something  not  given  in  experience 
which  leads  us  to  expect  a continuance  of  this  uniformity  in  some  cases  and 
not  in  others.  This  “ something,”  call  it  what  you  will,  is  what  we  are 
now  inquiring  after,  and  it  must  be  a priori. 


306 


LOGIC. PART  H. 


- - [CHAP. 

1126.  But  if  they  suggest  to  our  minds  these  classi- 
fications, it  must  be  because  they  proceeded  from  a 

implies  a creat  c^ass'concepti°n  Li  a mind  like  our  own,  at 
ing  mind  essen-  least  in  respect  to  the  faculty  of  constructing 

tially  like  ours.  x . . T P u -i  t 0 

such  conceptions.  It  the  words  I use  sug- 
gest to  the  mind  of  the  reader  or  hearer  a thought,  it 
must  be  because  they  proceeded  from  the  same  thought, 
and  are  used,  as  a means  of  expressing  it  in  my  own 
mind. 

1127.  Let  us  then  consider  the  operations  of  the 
An  analogy  in  human  mind.  Take  the  case  of  an  artisan. 

of  man.  lie  iorms  the  plan  ot  a piece  oi  mechanism, 
a watch  for  instance — that  plan  is  his  class-conception, 
his  object  being  not  to  produce  one  watch  only  but  a 
number — a supply  for  the  demand  of  his  customers. 
Hence  we  have  a species  of  watches  agreeing  exactly 
with  each  other,  so  far  as  the  properties  included  in  the 
class-conception  are  concerned,  hut  differing  in  the 
accidents  of  having  been  finished  at  different  times, 
by  different  hands  perhaps — made  in  part  of  different 
materials,  some  having  gold  and  others  silver  cases,  &c. ; 
and  differing  also  in  size  and  ornamental  decorations. 
How,  suppose  the  same  artisan  to  form  a different  plan 
or  class-conception,  one  differing  therefore  in  some  of 
the  essential  parts  of  a watch,  as  in  the  form  of  the 
escapement,  &c.,  and  we  shall  have  from  that  model 
another  species  of  watch. 

1128.  How  before  creation,  the  Creative  Mind  must 
The  class  con-  have  formed  such  class-conceptions  for  each 
creative  wind,  species  oi  created  objects;  and  each  nidi- 
vidual  in  a species  is  like  all  the  others  in  all  the  pro- 
perties which  were  included  in  that  class-conception  ; 
and  differing  from  others  only  in  those  which,  from 
their  not  being  included  in  the  original  class-concep- 
tion, are  called  accidental.* 

* This  illustration  of  the  operation  of  the  Divine  Mind  might  he  car- 
ried much  farther.  One  point  more  only,  however,  will  I notice  in 
passing. 

It  is  not  altogether  voluntary  with  man  what  elements  he  will  include 


in.]  METHODS  OF  PROOF  AND  REFUTATION . SECT.  V.  307 

1129.  We  may  then  say  that  the  uniformity  of 
Nature  consists  in  the  agreement  of  all  objects  Unilorm 
within  the  same  species  in  the  matter  of  their  in  ( of  Nature 
class-conception.  And  our  Induction  is  but 
the  process  by  which  we  make  our  conceptions  of  the 
material  species  adequate.  We  get  one  of  its  elements. 
We  classify  upon  that;  then  find  another  property 
common  to  all  the  individuals  in  that  species  which 
have  fallen  under  our  observation — predicate  this  latter 
property  of  the  species  by  means  of  the  specific  name 
which  we  have  given  it,  and  call  the  Proposition  so 
made  a statement  of  a law  of  Nature.  It  is  an  indica- 
tion of  the  Divine  will  and  conception  ; and  therefore 
we  expect  all  individuals  in  any  class  to  conform  to  the 
essentials  of  that  class — -which  essentials  we  are  learn- 
ing one  after  another  by  Induction.  If  there  were  no 
such  class-conception,  there  could  be  no  classification  ; 
no  Uniformity  of  Nature  ; consequently  no  Induction. 

in  his  class-conceptions.  Having  fixed  upon  some  which  are  material  to 
it,  there  are  othei-s  that  are  necessarily  implied,  and  others  that  are  acci- 
dental— over  which,  however,  he  has  no  control,  any  further  than  his  own 
hand  may  he  employed  in  making  the  objects  in  the  class.  Thus  in  a 
watch,  if  he  would  have  a lever  escapement,  he  must  have  a hair-spring, 
whether  he  would  or  not,  he  must  have  wheels  and  pinions  to  graduate  the 
motion ; and  he  must  have  the  liability  to  break,  to  wear,  &c.,  as  insepar- 
able from  all  the  materials  that  man  has  at  his  command  to  use.  And  as  all 
the  watches  of  that  species  are  to  be  made  by  himself,  or  under  his  control, 
he  can  control  the  purely  accidental  properties  of  size,  ornament,  &c.  But 
beyond  that  he  has  no  control  over  what  is  accidental. 

In  Nature,  however,  there  is  but  one  Creator  and  Producer.  All  those 
properties  of  the  objects  of  nature,  therefore,  which  so  far  as  we  can  see, 
are  only  accidental  to  the  class-conception,  are  yet  under  the  control  of  the 
Will  of  Him  who  designed  and  still  produces  them  ; and  in  all  of  them, 
therefore,  He  can  secure  a perfect  uniformity,  and  make  them  to  be  for  all 
practical  purposes,  not  accidental  but  essential. 

Hence  individuals  in  the  natural  species,  as  apples,  pears,  peaches,  dogs, 
horses,  men,  &e.,  &e.,  do  not  differ  so  much  from  each  other,  or  from  their 
idea  or  class-conception  as  the  works  of  man,  watches,  hats,  boots,  coats, 
&c.,  &c.,  nor  even  so  much  as  the  diagrams  which  we  draw  to  represent 
the  mathematical  figures,  triangle,  circle,  ellipse,  &c.,  differ  from  one 
another,  even  among  those  which  are  designed  to  represent  precisely  the 
same  conception.  Always  do  they  come  short  of  the  conception  to  some 
extent,  come  short  of  realizing  it  as  an  idea  ; and  go  beyond  it  in  present- 
ing to  the  mind  for  its  consideration,  properties  which  were  not  contained 
in  the  conception. 


308 


LOGIC. — PAKT  II. 


[CHAP. 


1130.  Now  whatever  is  necessary,  to  the  proof  of 
any  Proposition  is  in  some  way  a Premise  to  that 

whatever  is  Proposition.  Hence  the  Uniformity  of  Na- 
conecSn!°  is  ture  being  necessary  to  the  belief  in  the 
thatremconciu“  result  of  any  Induction,  that  uniformity 
sum.  must  enter  in  some  way  as  Premise  to  the 

Conclusion  from  the  Induction,  when  announced  as  a 
Law'  Of  Nature. 

1131.  Using  these  principles  as  Premises,  we  are 
induction  com-  able  to  complete  the  Induction  into  a Syllo- 

pleted  into  a r.  m d 

syllogism.  gism  as  follows,  ror  Major  Jr  remise  we 
have,  “All  similar  instances  in  Nature  are  governed 
by  the  same  law.” 

For  Minor  Premise  we  may  say,  “ The  cat,  the  dog, 
the  wolf  are  instances  of  carnivorous  animals,  similar 
in  having  canine  teeth.” 

.•.  All  animals  with  canine  teeth,  will  be  instances 
of  the  same  law,  viz.,  carnivorous  animals — that  is, 
“ All  animals  with  canine  teeth  will  be  carnivorous.”  * 

1132.  But  if  the  Major  Premise  were  removed  or 


* It  lias  been  pretty  extensively  held  that  Induction  is  a Method  of 
Argumentation  totally  unlike  the  Syllogistic,  and  one  which  can  never  be 
reduced  to  a Syllogism.  Sir  William  Hamilton  was  of  this  opinion.  Now 
there  can  be  no  doubt  that  Induction,  as  a Method  of  Investigation,  is  a Me- 
thod radically  different  from  Deduction  or  the  Syllogism.  But  the  Induc- 
tion, as  an  investigation  of  the  predicates  of  Natural  Species,  is  a very  dif- 
ferent thing  from  the  verification  of  that  Method,  or  the  use  which  we 
make  of  the  Induction  as  a means  of  proof.  The  Binomial  theorem  is  one 
thing,  the  use  we  make  of  it  in  practice  quite  another — and  the  reasoning 
and  principles  by  which  we  verify  the  theorem  is  another  still — and  quite 
as  distinct  from  the  theorem  itseif. 

Now  Methods  of  Investigation  cannot  be  reduced  to  the  Logical  For- 
mula. The  Formulae  are  the  Means  to  be  used  in  the  Methods  of  Proof, 
and  whatever  can  be  proved  must  be  proved  by  some  Formula — one  that 
has  been  catalogued  and  examined,  or  one  that  yet  remains  to  be  entered 
upon  our  list.  But  Methods  of  Investigation  prove  nothing. 

There  can  be  no  need  of  the  accumulation  of  authorities  or  of  argument 
to  show,  not  that  the  Induction,  but  that  our  confidence  in  its  results — 
and  hence  Induction,  as  a Method  of  Proof,  depends  upon  the  uniformity 
of  Nature.  This  point  is  nowhere  denied  or  doubted.  If  this  be  so,  this 
Uniformity,  stated  as  a Principle  or  Premise,  must  be  the  Major  Premise 
in  all  Proof  from  Induction  ; and  the  basis  of  the  verification  of  Induction 
itself  as  a Method  of  Investigation. 


III.]  METHODS  OF  PROOF  AND  REFUTATION. — SECT.  Y.  30& 


denied,  no  confidence  whatever  would  be  placed  in  the 
Conclusion.  That  is,  take  away  the  Uni-  ^ Inductjon 
formity  of  Nature,  and  we  should  place  no  withouttheMa- 
confidence  in  Induction  as  a means  of  Proof,  Jor 
or  as  indicating  a law  upon  which  we  could  base  any 
predictions  or  expectations  for  the  future. 

1133.  We  have  seen  that  Induction  is  the  Method 
which  most  appropriately  belongs  to  the  facts  in 
the  reality  of  being,  and  within  the  range  Inductjon  be 
of  what  is  called  Nature — including  as  it  longs'  to  Physi- 
does  all  facts  which  are  not  considered  as  CJ  1 d er' 
depending  directly  upon  the  will  and  volitions  of  a 
moral  agent.  But  inasmuch  as  the  will  of  man  is 
subject  to  no  such  law  of  necessity  and  uniformity,  as 
the  course  of  Nature,  and  inasmuch  as  the  courses  of 
events  in  God’s  providential  government  of  the  world 
are  to  such  an  extent  above  our  knowledge  Butr.ottoMo- 
and  comprehension,  the  facts  or  events  in  ralMatter- 
each  of  these  two  Spheres  are  hardly  to  be  considered 
as  within  the  province  of  Induction.  W e can  indeed 
in  this  way  learn  much  of  the  nature  of  man,  and  of 
the  plans  and  principles  of  God’s  moral  government, 
hut  not  enough  to  enable  us  to  speak  with  the  same 
confidence  as  we  may  use  in  regard  to  the  facts  of 
Nature.  That  God  is  just,  we  know  indeed  as  well  as 
we  know  any  truth  of  Natural  Science,  and  that  He 
will  punish  any  particular  sin  we  may  also  know  with 
the  same  certainty.  But  the  particular  time,  way,  and 
means  we  cannot  infer  from  any  induction  of  the  past 
with  any  thing  that  approaches  a physical  certainty. 

1134.  So,  too,  from  an  observation  of  human  nature, 
we  see  that  men  for  the  most  part  are  gov- 

erned  m their  actions  by  a regard  to  their  destroys  uni- 
own  interests.  But  we  cannot  therefore  say, 
in  any  particular  case,  with  any  thing  like  the  certainty 
of  an  induction,  that  this  man  will  be  -controlled  by 
considerations  of  self-interest.  There  are  not  only  too 
many  exceptions  to  the  rule  to  allow  • of  such  a cer- 
tainty, but  we  recognize  in  all  men  a capacity  to  resist 


310 


LOGIC. PABT  n. 


[chap. 


all  sucli  considerations  whenever  they  choose  to  clo  so  ; 
not  only  for  the  purpose  of  following  their  passions,  but 
also  in  many  cases  for  the  heroic  purpose  of  sacrificing 
themselves  and  their  own  interests  for  the  truth  and 
the  good  of  others. 

1135.  The  next  condition,  limiting  the  sphere  of 

Induction,  is  that  the  Predicate  be  not  an  Accidental 
induction  can-  property,  hut  such  as  are  regarded  as  inse- 
dentai°vproper-  pcirable  properties.  Induction  does  not  ex- 
ties-  tend  to  separable  accidents  or  properties. 

If  they  are  inseparable  it  is  because  there  is  some  law 
or  necessity  connecting  and  binding  them  to  a con- 
comitance with  the  more  obvious  properties  which 
make  up  the  Essentia  of  the  class-conception.  But  if 
they  are  separable  their  connection  with  the  indivi- 
duals of  the  genus  is  regarded  as  merely  accidental, 

implying  neither  necessitv  nor  law  ; and  the 
considered  acci-  connection  remains,  tor  the  present  at  least, 
found  tcTbe  ese  an  isolated  fact.  Further  discoveries,  how- 
ever, may  find  relations  which  indicate  law 
and  design,  and  then  a new  genus  will  be  formed  to 
which  this  property  will  no  longer  be  an  accident  but 
an  inseparable  property. 

1136.  But  until  that  is  done  and  we  gain  some  in- 
sight into  the  will  and  designs  of  Providence,  farther 
than  the  mere  Induction  of  facts  can  give,  we  hardly 
call  our  investigation  an  Induction  at  all.  Thus  M. 

Cousin  lias  observed  that  great  events  take 
trat?onftom his-  place  in  the  middle  of  centuries.  He  speaks 
of  the  Middle  of  the  Fourteenth  as  remark- 
able for  the  discoveries  and  revival  of  learning ; the 
Fifteenth  as  remarkable  for  the  fall  of  Constantinople  ; 
the  Sixteenth  for  the  Reformation  ; the  Seventeenth 
for  the  English  Rebellion,  &c. ; and  yet  no  one  regards 
this  as  an  induction  establishing  a law,  that  the  middle 
of  every  century  will  be  accompanied  by  some  great 
event  in  history.  Again,  five  of  the  Presidents  of  the 
United  States — the  first  five,  went  out  of  office  when 
they  were  sixty-six  years  old.  No  one  regards  this. 


HI.]  METHODS  OF  PROOF  AND  REFUTATION. — SECT.  V.  311 


however,  as  an  induction  that  establishes  a general 
fact  or  law,  that  all  Presidents  shall  hold  office  until 
they  are  sixty-six  years  old. 

1137.  And  yet  there  is  undoubtedly  an  important 

sense  in  which  the  facts  of  History  constitute  Facts  of  His. 
a field  for  inductive  investigations.  jgfo 

One  of  the  most  striking  and  extraordi-  for  rnduction- 
nary  illustrations  of  this  that  I have  ever  seen,  is  Spel- 
man’s  History  and  Fate  of  Sacrilege ; in  which,  after 
deducing  the  law  of  God  upon  the  subject  from  the 
Scriptures,  he  runs  over  the  whole  of  History,  and 
especially  the  History  of  England  since  the  Reforma- 
tion, to  show  how  the  facts  of  History  indicates  prin- 
ciples the  same  as  those  educed  from  the  Scriptures. 

1138.  This  use  of  History  assumes  that  God  has  a 
plan  and  a purpose  in  History,  and  governs 
the  moral  world  by  laws  as  completely  as 


He  does  the  natural  world ; and  that  from 


This  use  of 
History  assumes 
a Moral  Govern- 
ment of  the 
world. 


the  facts  evolved,  His  will  can  be  learned  in  the  one 
case  as  certainly  as  in  the  other. 

1139.  Induction,  therefore,  becomes  a ground  of 
Proof,  or  belief  in  the  result  obtained  by  our  induction  ap- 
classification,  only  as  it  approaches  to  the  Demonstration, 
condition  in  which  we  could  demonstrate  the  .conclu- 
sion which  we  reach  by  our  inductive  investigation 
from  the  class-conception.  In  Mathematics  we  get  the 
class-conception  by  constructing  in  our  own  mind  the 
figures  which  are  comprehended  under  it.  But  before 
the  creation  of  the  world,  the  Creator  must  have  con- 
structed the  same  class-conception  of  all  objects  to  be 
comprehended  under  each  species  of  being  that  He 
would  create.  These  conceptions  are  what  Plato  called 
Ideas,  and  Aristotle  called  Motions  {ra  vorjTa),  or  as 
we  render  the  word,  “ conceptions.” 

• 1139.  Induction  helps  us  to  these  Ideas  or  Concep- 
tions, and  puts  us,  so  far  as  it  is  successful,  Induction  lim. 
into  the  position  which  the  Creative  Mind  e£ 

occupied  with  regard  to  them  before  crea-  “nlm "iud  S® 
tion.  It  puts  us  into  the  same  relation  in  “““ptions. 


312 


LOGIC. PART  II. 


[CHAP. 


regard  to  objects  in  the  natural  world  as  we  sustain 
to  the  Figures  of  Geometry,  which  we  have  constructed 
in  our  own  imagination,  or  those  conceptions  of  the 
various  machines  and  implements  of  human  contriv- 
ance with  which  the  abodes  of  civilized  man  every 
where  .abounds.  And  from  the  matter  of  the  Ideas  or 
class-conceptions,  as  Material  Properties,  we  see  that 
other  properties  are  necessarily  implied.  And  it  is  a 
matter  of  doubt  if  there  is  or  can  be  any  Induction 
which  deserves  to  be  so  called — that  undertakes  to 
prove  any  property  of  a species  in  natural  objects 
which  is  not  implied  in  the  Matter  of  its  class-concep- 
tion, as  that  conception  existed  in  the  Creative  Mind.* 


* Since  these  pages  were  put  into  the  Printer’s  hand,  I have  met  with  a 
report  of  the  doings  of  “ the  American  Association  for  the  Advancement  of 
Science ,”  lield  at  Providence,  R.  I.  In  the  report  of  the  doings  for  August 
16th  [1855],  there  is  an  account  of  Prof.  Agassiz’  paper  of  “ The  System 
in  Zoology,”  from  which  I make  the  extract  below. 

I have  long  regarded  Prof.  Agassiz  as  the  most  philosophical  of  all  our 
naturalists ; perhaps  more  so  than  any  other  scholar  in  that  department  now 
living.  And  it  affords  me  great  pleasure  to  find  that  after  some  twenty 
years  study  and  effort  at  an  attempt  to  classify,  and  so  proceed  with  his 
Induction  on  some  other  principle  than  that  to  which  I had  arrived  on  phi- 
losophical grounds,  he  has  at  last  found  by  his  experience  that  it  is  impos- 
sible to  do  so.  And,  aside  from  the  pleasure  which  it  affords  me  as  a con- 
firmation.of  my  view  on  the  subject,  I cannot  hut  regard  his  announcement 
as  not  only  a great  triumph  of  philosophy  in  general,  hut  also  of  Christian 
Faith  in  particular. 

I give  his  words  as  I find  them  in  the  Report  (N.  Y.  Daily  Times,  Aug. 
18,  1855).  Even  the  Italics  are  given  as  I copy  them. 

“ Even  as  late  as  the  last  classification  of  the  animal  kingdom  by 
Cuvier — a system  which  has  made  his  name  so  famous — that  distinguished 
naturalist  depended  more  upon  arbitrary  groupings  than  upon  critical  ob- 
servations of  natural  affinities.  To  be  understood  well,  the  true  relations  of 
the  system  o"f  Nature  ought  to  be  considered  as  an  analysis  of  the  thought  ex- 
pressed by  the  Creator.  Classification  is  in  reality  nothing  but  the  expression  of 
that  thought.  We  may  no  longer  speak  of  our  system.  We  may  only  speak  of 
our  readings  of  that  thought  which  constitutes  the  animal  system  ; which 
has  gone  on  developing  through  countless  ages.  No  longer  do  naturalists 
consider  the  Animal  Kingdom  without  reference  to  the  cause  of  existence. 
They  are  ail  driven  to  one  point.  They  are  compelled  to  ascribe  existence 
of  animal  forms,  either  to  physical  causes  or  to  an  intelligent  Maker.  Be- 
tween these  two  there  is  no  medium  point,  no  other  alternative.  The 
classes  of  animals  are  either  the  result  of  the  general  forces  which  we  ob- 
serve in  Nature,  or  they  are  the  work  of  an  intelligent  Being.  Do  we  see 
in  these  classes  the  evidences  of  physical  force — or  thought ! And  now, 


HI.]  METHODS  OF  PROOF  AND  REFUTATION. — SECT.  V.  313 

Thus  if  carnivorousness  was  an  element  in  the  class-con- 
ception of  the  Canidse,  just  as  equality  of  radii  is  in 
that  of  the  circle,  then  canine  teeth  were  as  necessarily 
implied  as  a property  of  the  Canidse,  as  the  Formulae 
and  Propositions  of  Trigonometry  are  in  the  conception 
of  the  Triangle. 

1140.  We  can  also  accomplish  our  object  of  passing 
from  the  facts  of  Nature  to  a law  by  means  We  may  als0 
of  the  conception  of  Final  Causes.  A Final  §f|wfbymeaS 
Cause,  as  has  been  defined,  is  that  for  which  ofFiaal  cl|es- 
any  thing  is  or  is  done. 

1141.  We  are  conscious  of  acting  from  purpose  or 
design.  Our  actions  are  conformed  to  our  0rigin  of  the 
designs  and  reveal  them  to  others.  We  can  Icdaease3ofinFtyl 
also  see  in  the  motions,  features,  and  acts  of  ture- 
other  persons  indications  of  their  designs.  We  can 
often  see  in  the  structure  of  a piece  of  machinery  or 
an  implement  of  any  kind,  the  design  which  its  framer 
intended  and  expected  it  should  accomplish. 

1142.  Precisely  so  in  Nature  we  see,  and  cannot 
help  but  see  marks  of  design — proofs  that  the  Nature  indi. 
Creator  had  an  end  in  view — that  He  created  cates  Design- 
from  regard  to  Final  Causes.  If  now  we  find  by  our 
induction  that  animals  with  canine  teeth  are  carnivo- 
rous, and  can  moreover  see  that  that  kind  of  teeth  are 
especially  adapted  to  that  kind  of  food,  we  have  scarcely 
less  doubt  that  all  animals  with  canine  teeth  are  carni- 
vorous, than  if  we  had  seen  them  all  in  the  pursuit  of 
that  mode  of  life — or  if  the  Omniscient  Creator  Him- 
self had  revealed  to  us  the  fact. 

1143.  When  then  our  induction  leads  us  to  see  any 
connection  between  the  Essentia  of  the  Ge-  Final  Causes 
nus  and  the  Property  predicated  of  it,  as  is  based  upon  the 
implied  in  the  doctrine  of  Final  Causes,  or  creator 

as  the  necessary  correlates  of  each  other,  we  feel 

when  we  come  to  consider  the  Animal  Kingdom  practically,  as  a process  of 
Zoological  Investigation,  it  comes  first  in  order  to  ascertain  whether,  in  the 
combinations  already  ascertained,  we  can  read  that  thought,  or  whether  any 
other  result  can  there  he  read.” 


14 


314 


LOGIC. — PAHT  II. 


[chap. 


confident  that  we  have  found  a law,  which  if  it  he  not 
based  upon  the  necessary  nature  of  the  things,  is  at 
least  based  upon  the  will  of  the  Creator,  and  will  not 
therefore  be  changed  while  the  present  order  of  things 
remains. 

1144.  But  so  expressive  are  the  works  of  Nature 
every  where  of  purpose  and  design,  that  long  before 

Nothing  made  we  come  to  conscious  reflection  upon  the 
m vain.  subject,  we  have  come  to  believe  that  what- 
ever exists  as  the  work  of  the  Creator,  was  made  for 
some  purpose,  or  “ Nothing  was  made  in  vain.”  The 
Formal  properties — that  is,  those  properties  in  any 
object  which  are  regarded  as  constituting  it  an  indi- 
vidual in  the  species  between  itself  and  the  next  sub- 
altern species  or  genus,  which  is  in  our  minds  at  the 
time,  put  us  on  the  inquiry  to  ascertain  what  are  the 
implied  properties  which  accompany  these  Differentia 
or  Formal  properties;  and  what  are  they  for;  what 
fact  or  law  in  regard  to  the  individuals  of  their  class 
do  they  indicate. 

1145.  Now  this  way  of  regarding  the  Formal  pro- 
perties of  objects  is  not  the  result  of  any  system  of  phi- 

The  idea  of  losophy.  It  exists  before  philosophy.  One 
eS  before  of  the  first  questions  that  the  child  learns  to 
philosophy.  ask  with  regard  to  any  thing  new  that  at- 
atracts  its  attention  is,  “What  is  it  for?”  Thus  to 
take  the  case  already  spoken  of — we  see  certain  ani- 
mals with  teeth  of  a peculiar  shape  ; we  see  one  of 
them  using  these  teeth  to  tear  the  flesh  of  some  animal 
which  it  has  just  caught,  and  devouring  that  flesh  as 
food.  The  adaptation  of  the  teeth  to  the  end  for  which 
we  see  them  being  used,  is  such  that  we  have  no  doubt 
that  such  Avas  their  design  or  Final  Cause. 

1146.  One  case  is  enough.  It  seems  to  let  us  into 
one  case  suffi.  the  secrets  of  Nature — the  counsels  of  the 
the"bei°ief!ssest  Creator.  We  feel  as  though  we  knew  why 
He  had  so  made  the  animal ; and  we  predicate  that 
mode  of  life  of  all  animals  having  the  same  Formal 
property,  as  a general  fact.  We  hold  it  as  a physical 


m.]  METHODS  OF  PROOF  AND  REFUTATION. — SECT.  V.  315 


certainty — but  not  $s  an  absolute  certainty.  For  not 
only  may  tlie  nature  or  formal  properties  change  in 
some  respects,  but  influences  may  exist  in  some  cases 
which  will  turn  individuals  and  even  whole  species 
from  the  course  of  nature. 

1147.  There  are  sometimes  cases  of  individual  de- 
formity. Most  of  the  species  of  domesticated  Cases  of  de. 
animals  have  been  changed  by  domestica-  fonnity- 
tion ; and  some  of  them  so  much  that  it  is  now  diffi- 
cult to  ascertain  precisely  what  they  were  in  their 
undomesticated  state.  Man,  we  see  was  made  for  vera- 
city, benevolence,  and  virtue ; but  his  history  shows 
that  there  has  been  a very  general  departure  from  what 
his  nature  shows  that  he  was  intended  for. 

1148.  The  Fundamental  Principle  of  this  doctrine 
of  Final  Causes  is,  that  whatever  exists  in 

-i  • t*  -\t  i . . ry  -i  Fundamental 

tlie  domain  oi  JN  ature  exists  lor  some  end  or  Principles  in 

-i  . ■ , , • this  doctrine. 

purpose,  and  consequently  where  its  consti- 
tution  and  use  indicates  a purpose,  we  infer  that  that 
was  the  purpose  designed,  and  consequently  the  law 
of  its  being  which  was  imposed  upon  it  by  its  Creator, 

1149.  Now  taking  this  Principle  for  our  Major 
Premise  and  we  have  : 

That  for  which  any  thing  in  Nature  was  evidently 
designed  it  will  accomplish. 

Canine  teeth  were  evidently  designed  for  a carni- 
vorous habit  of  life. 

Therefore , Animals  with  canine  teeth  will  always 
be  carnivorous. 

1150.  Hence  as  Induction  always  implies  that 
whatever  is  or  occurs,  is  or  occurs  for  some  Induction  ai- 
purpose  or  design ; so  it  implies  also  a ^hntd^ent 
Wisdom  which  comprehends  all  things  and  Creator- 
events,  and  never  errs — and  a Power  which  can  ac- 
complish all  that  that  Wisdom  can  design. 

1151.  In  the  domain  of  Nature  it  is  immaterial,  so 
far  as  the  result  is  concerned,  whether  we  In  Phy9ica,  Mat. 
begin  with  the  constitution  of  the  object  as  ftom'eCdairepfo“ 
seen  in  its  Formal  Properties,  or  with  the  £ear^ees  10  theFina‘ 


316 


LOGIC. — PART  II. 


[chap. 


Final  Cause  as  seen  in  its  Modal — -the  result  is  in  each 
case  and  alike  the  same.  But  with  man  it  is  not  so. 
We  see  from  his  constitution  that  he  was  designed  for 
But  not  in  Mo-  virtue.  But  we  see  much  in  his  Modal  pro- 
ral-  perties — that  is,  in  his  thoughts,  feelings, 

and  actions- — that  is  not  in  accordance  with  the  Final 
Cause  of  his  being ; much  which  therefore  we  pro- 
nounce to  be  wrong,  or  at  least  abnormal. 

1152.  So  too  in  Nature,  there  are  abnormal  cases 
in  which  we  cannot  infer  from  the  individual  the  de- 
Abnormai  cases  sign  or  law  °f  the  m|fde  of  life  which  his 
in  Nature.  species  was  intended  to  pursue.  If  we  should 
find  a man,  without  legs  from  his  birth,  it  would  not 
answer  to  infer  from  him  that  all  men  were  designed 
merely  to  sit  or  to  crawl,  and  that  walking  is  a viola- 
tion of  the  law  of  man’s  being.  Such  anomalies  occur 
in  nearly  all  species  of  being.  And  FIugh  Miller* 
has  suggested  that  there  may  be,  and  that  in  fact  there 
are  reasons  for  believing  that  there  are,  in  Nature 
whole  species  which  have  been  degraded  from  their  idea 
or  normal  condition.  Of  such  he  thinks  that  serpents, 
venomous  insects,  and  insects  with  stings,  are  exam- 
ples. His  remark  would  include  all  those  which  have 
means  of  injury  to  other  beings  not  necessary  as  either 
means  of  defence  or  of  taking  their  prey. 

1153.  The  Argument  from  Examples,  or  a Fact  as 
an  Example,  is  evidently  but  an  induction  from  a sin- 

Fac,3  as  Ex.  gle  inducted  fact ; as  when  we  argue  from 
ampies.  the  fact  that  Astronomy  was  opposed  by 
religious  bigotry,  when  it  first  began  to  be  cultivated 
by  the  Christian  Philosophers  in  the  Middle  Ages, 
that  Geology  will  be  in  like  manner  opposed  as  sub- 
versive of  the  Christian  faith. 

1151.  It  is  evident  that  the  particulars  denoted  by 
the  terms  “ Astronomy  ” and  “ Geology  ” in  this  case, 
There  must  be  must  have  a resemblance,  consisting  of  iden- 
J.oinFof'com'i  tity  in  the  properties  on  which  the  compari- 
parison.  son  or  argument  is  based.  And  in  estimat- 


Old  Red  Sandstone,  final  Chapter. 


HI.]  METHODS  OF  PROOF  AND  REFUTATION. — SECT.  V.  317 


ing  the  force  of  an  Argument  of  this  kind,  the  first  step 
in  each  case  is  to  consider  whether  there  really  is  that 
resemblance  or  identity  or  not. 

1155.  But  we  are  at  present  concerned  only  with 
the  Method  and  its  proper  force.  The  Argument  stated 
in  brief  is  this  : 

Astronomy  when  first  introduced  was  opposed  as 
adverse  to  religion. 

.•.  Geology  when  first  introduced  will  be  opposed 
as  adverse  to  religion. 

1156.  This  is  manifestly  an  Enthymeme,  in  which 
the  Minor  Premise  is  suppressed. 

A is  P, 

.-.  G is  P. 

We  may  complete  the  Formula  by  affirming  A of  G. 
Thus, 


A is  P, 

G is  A, 

.•.  G is  P ; 

that  is,  by  saying  that  “ Geology  is  Astronomy.”  But 
that  is  not  true.  Astronomy  and  Geology  are  not  iden- 
tical ; nor  is  Astronomy  a species  within  which  Geo- 
logy is  included.  All  we  can  say,  and  all  that  the 
Argument  from  Example  means  to  say,  is  that  they  are 
alike.  But  as  this  does  not  affirm  either  identity  of 
spheres,  or  include  the  one  in  the  other,  no  inference 
can  be  drawn  by  means  of  such  a proposition  in  a 
categorical  Syllogism. 

1157.  The  Force  of  the  Argument  from  Facts  as 
Examples,  therefore,  must  be  sought  in  the  The  Inference 
point  of  resemblance,  considered  as  the  thatfdentity1!011 
Formal  Properties  of  a Species. 

Thus  Astronomy,  when  first  introduced,  was  a new 
science,  contradicting  some  of  the  prevailing  theologi- 
cal opinions. 

But  Astronomy  was  opposed  by  the  religious  when 
first  introduced,  because  it  contradicted,  &c. 

Therefore  all  sciences  which  contradict  the  preva- 
lent theological  notions,  will  be  opposed  when  first 
introduced. 


318 


LOGIC. — PART  H. 


[CHAP. 


1158.  With  this  Conclusion  for  a Major  Premise, 
we  introduce  “ Geology  is  a new  science,  contra- 
dicting the  prevalent  theological  notions ; ” and  we 
have  the  conclusion,  therefore  “ Geology  will  be  op- 
posed,” &c. 

1159.  It  will  he  seen  that  in  form  this  is  but  an 
iJS'nefrom  I11^110^011  from  a single  Example  as  an  in- 
a single  Fact.m  ducted  fact,  and  as  such  depends  for  whatever 
value  it  may  have  either  as  a Method  of  Investigation 
or  of  Proof,  upon  the  principles  and  laws  of  Induction, 
and  the  extent  to  which  it  fulfils  them.* 

1160.  This  Method  is  seldom,  if  ever,  spoken  of  in 
except  common  use  °f  language  as  an  Argument 

inM^aiMatfer  from  Example,  except  when  it  is  applied  to 
Moral  Matter.  In  that  case  the  value  of  the  Method 
is  much  less,  since  there  is  no  such  uniformity  of 
Causes  and  Laws  in  Moral  as  in  Physical  Matter. 


* Whatf.ly,  in  liis  Rhetoric,  Part.  I.  Chap.  II.  § 6,  has  given  the  Ar- 
gument from  Example  in  a form  which  is,  perhaps,  more  striking  than  that 
in  the  text,  as  follows  : 


Astronomy  was  decried  at  its  first 
introduction  as  adverse  to  religion  : 

I 

% 

Ob  . 

Every  science  is  likely  to  be  decried 
religion. 


Geology  is  likely  to  be  decried, 
&c. : 


its  first  introduction  as  adverse  to 


But  this  Major  Premise  is  untrue,  and  can  be  saved  only  by  the  Modal, 
inserted  above  : “ Every  science  which  contradicts  the  prevalent  religious 
opinions — •”  In  this  case  the  Modal  not  only  limits  the  subject  to  an  included 
species,  hut  is  also  in  fact  assigning  the  Cause,  and  we  might  therefore  have 
the  Causal  Argument. 

Astronomy  was  decried  because  it  opposed  the  prevalent  religious 
opinions. 

Geology  opposes  the  prevalent  religious  opinions. 

.•.  Geology  will  he  decried. 

And  in  fact  the  inference  of  a General  Principle-  from  a single  fact  as 
Example,  or  many,  as  inducted  particulars,  must  always  be  limited  in  one 
of  these  two  ways — namely,  either  to  instances  of  the  same  kind  only,  or  to 
instances  in  which  the  same  cause  is  at  work  upon  matter  which  is  essen- 
tially the  same. 


m.]  METHODS  OF  PROOF  AND  REFUTATION. SECT.  Y.  319 

1161.  The  Induction  of  Facts  by  way  of  Example, 
is'  but  a loose  and  vague  way  of  reasoning,  Argumentfrom 
and  is  seldom  satisfactory.  For  in  all  con-  fommplatis&£ 

. tingent  matter,  that  there  are  exceptions  to  tory- 
all  rules  is  proverbial ; and  the  Argument  from  Exam- 
ple often  has  the  appearance,  and  is  in  danger  of  the 
reality,  of  being  based  upon  the  exceptions  rather  than 
upon  the  individual  facts  coming  under  the  Rule.  Thus 
if  one  should  attempt  to  prove  from  Examples  of  dreams 
coming  to  pass,  that  dreams  are  to  be  regarded  as 
generally  prophetic,  or  signs  of  what  is  to  take  place, 
he  would  most  manifestly  be  arguing  from  the  exception 
to  the  general  rule.  Yet  Examples  of  what  he  is  trying 
to  prove  can  undoubtedly  be  produced.  Nor  in  fact 
is  there  any  proposition  in  Contingent  Matter,  however 
absurd,  which  may  not  find  some  Minor  Premise, 
which  by  way  of  Example,  will  connect  it  in  the  fulfil- 
ment of  Formula  with  some  indisputable  Major  Pre- 
mise, and  thus  prove  it  to  be  true  with  all  the  force  of 
which  the  Argument  from  Example  is  capable. 

1162.  Two  affirmative  Premises  in  the  2d  Figure 
constitute  an  Analogy  between  their  sub-  Ana,0„y  how 

ieCtS.  AS,  constituted. 

A is  B, 

C is  B. 

A and  C must  therefore  be  analogous,  or  identical 
in  the  Matter  of  the  conception  B. 

1163.  But  if  we  take  that  Matter  as  a Formal  Pro- 
perty, and  then  predicate  of  A or  C some 

other  Modal  Property  in  a compound  Causal,  perty  taken  as 
assigning  B as  its  Cause,  we  may  predicate  LJll“e' 
that  Property  also  in  an  Argument  from  Analogy  of 
the  other  of  those  subjects.  Thus, 

A is  C, 

Bis  C. 

But  A is  X because  it  is  C, 

.-.  B is  X. 

1161.  Thus  Bishop  Butler  argues  from  the  analogy 
between  the  death  of  man  and  the  chrysalis  state  of 


320 


LOGIC. — PART  II. 


[chap. 


This  Argument  put  into  Form  would  stand 


the  worm,  that  the  soul  of  man  is  immortal.  The* 
Bishop  Butiefs  chrysalis  and  the  man  have  hut  few  points 
argument.  jn  common.  Yet  some  such  points  or  pro- 
perties they  have — and  the  analogy  is  in  this  case 
somewhat  remote  ; and  in  consequence  requires  much 
greater  scrutiny,  and  can  never  in  fact  produce  the 
same  degree  of  certainty  as  the  closer  analogies. 

1165  ” ‘ ‘ ‘ 

thus  : 

Man  has  a principle  of  life. 

The  worm  has  a principle  of  life. 

The  worm  lives  through  an  apparent  death,  because 
comePi1tIdment  it  has  the  principle  of  life. 

Therefore  man  will  live  through  the  appearance 
of  death  at  the  dissolution  of  his  body. 

1166.  Or  without  the  Causal  we  may  have  the 
problematic  Problematic  Conclusion,  (which  is  in  all 
conclusion.  cases  valid  of  the  Affirmative  Premises  in 
the  2d  Figure,) 

Therefore  man  may  live  through  the  apparent  ex- 
tinction of  his  being  at  the  death  of  his  body. 

1167.  There  is  sometimes  a presumption,  but  no- 
thing more,  arising  from  the  fact  that  two  individuals 

Analogy  in  which  are  known  to  agree  in  many  points  as 
aiways0,atssa?is  a common  Essentia,  will  agree  in  a certain 
encel'o 'analogy  other  point  in  regard  to  which  it  is  not  yet 
mothers.  known  whether  they  agree  or  not.  Put 
arguments  based  on  such  supposed  analogies  are  of  hut 
little  value.  Thus  a man  and  a horse  agree  in  a vast 
number  of  points  of  the  animal  economy,  but  still  they 
may  disagree  in  regard  to  that  property  by  which  a 
certain  plant  is  food  for  one  and  a poison  for  the  other. 
The  probability  is  against  any  such  proposition  on  the 
ground  of  general  analogy,  hut  still  it  is  only  a proba- 
bility ; and  the  proposition  may  he  true,  as  we  know 
that  it  is  true  in  a vast  number  of  instances. 

1168.  The  reason  for  the  inferiority  of  the  Argument 
why  Analogy  from  Analogy  to  an  Induction,  results  as  will 

induction.  be  seen  irom  the  inadequacy  oi  the  class- 


ni.]  METHODS  OF  PROOF  AND  REFUTATION. SECT.  V.  321 

conceptions  which  we  have  in  onr  own  minds — an 
inadequacy  which  Induction  and  Analysis  properly 
used  are  all  the  while  removing,  and  the  removal  of 
which  converts  the  Induction  into  Demonstrative 
Sciences  just  as  fast  as  it  progresses. 

1169.  There  is  another  use  of  Analogy  which  is  of 
great  value,  and  which  we  ought  not  to  fail  Anaiogy  as  a 
to  notice  in  this  place.  It  consists  in  remov-  “meet- 
ing antecedent  objections  and  improbabili-  dent objections, 
ties,  in  interposing  objections  to  too  hasty  inductions, 
or  inferences  from  inductions  too  broad  for  the  inducted 
facts. 

1170.  Any  inference  which  is  too  broad  for  the 
facts — that  is,  an  inference  including  a Genus  m what  way. 
comprehending  several  species  from  facts  gathered 
from  one  species  alone,  must  comprehend  the  facts  of 
the  other  species  also  as  being  necessarily  analogous 
to  the  extent  of  their  common  Essentia.  If,  therefore, 
such  analogous  facts  can  be  adduced,  which  are  not  in 
accordance  with  the  inference,  they  are  an  answer  to  it. 
This  is  the  case  with  Butler’s  Analogy.  It  refutes  the 
Major  Premise  of  the  sceptic,  by  substituting  a new 
Minor  Term,  “ the  Chrysalis  ” for  “ Man  ; ” and  with 
the  same  Middle  and  Major  Terms,  the  Bishop  deduces 
a Conclusion  which  is  contradictory  to  an  indisputable 
fact.*  But  as  the  new  Minor  Premise  cannot  be  dis- 
puted, the  Major  Premise  is  proved  thereby  to  be 
untrue,  and  consequently  the  inference  from  it  to  the 
death  of  the  soul  of  man,  is  invalid. 

* The  Infidel  had  inferred  from  the  appearance,  that  man’s  being  ter- 
minated at  the  death  of  the  body.  His  argument  was  that : 

Man  appears  to  end  his  being  at  death. 

Therefore  his  being  does  end,  and  the  immortality  of  the  soul  is  but  a 
dream. 

But  the  Bishop  says,  Your  principle,  Major  Premise,  proves  too  much ; 
for  the  worm  when  it  goes  into  the  chrysalis  state,  appears  to  die,  as  evi- 
dently as  man,  and  yet  the  worm  comes  out  a butterfly.  Man  may,  there- 
fore, notwithstanding  the  appearance,  come  out  of  the  apparent  death 
a purely  spiritual  being,  with  powers  and  faculties  which  he  does  not  nowT 
possess. 


11* 


322 


LOGIC. PART  II. 


[chap. 


1171.  In  the  same  way  the  antecedent  objection  to 
a miraculous  revelation  of  the  will  of'.God  in  Cliristian- 

Removes  also  i ty , is  answered  by  the  fact  that  there  has 
fencu™dtonRe°e-  been  an  interposition  at  the  creation  of  man ; 
latl0n-  and  if  there  has  been  one  such  interposition, 

there  can  be  no  antecedent  presumption  against  an- 
other’s being  made  when  there  is  sufficient  occasion 
for  it. 

1172.  Both  Testimony  and  Circumstances  are  to  be 
Testimony  and  regarded  by  Logic  as  Facts.  The  reality  and 

Circumstances  V pi*i*t*i  n i ji 

as  Facts.  value  oi  which,  individually  and  separately, 
are  to  he  determined  by  principles  which  do  not  belong 
to  the  sphere  of  Logic.  But  the  force  of  concurrence  in 
testimony  and  in  circumstances,  is  a fact  which  it 
becomes  important  to  consider  in  this  connection. 

1173.  By  Concurrence  we  understand  such  a con- 
concurrence.  nection  between  two  or  more  circumstances, 
or  pieces  of  testimony,  as  that  one  did  not  cause 
the  other ; nor  does  the  one  serve  to  explain  and 
account  for  the  reality  of  the  other,  except  through  or 
by  means  of  the  principle  which  they  are  adduced  to 
ptrove. 

1174.  Thus  two  witnesses  testifying  in  the  presence 
of  Testimony  of  each  other,  or  after  an  interview  between 

accumujated.  them  on  the  subject  ot  their  testimony,  could 
hardly  give  what  would  be  fairly  considered  concurrent 
testimony.  It  would  be  accumulated  testimony,  and 
worth  just  as  much  additional  force  as  the  moral  char- 
acter of  the  second  witness,  and  his  opportunity  to 
know  could  give  it.  But  the  testimony  of  the  second 
might  be  accounted  for  on  the  ground  that  he  knew 
what  was  the  testimony  which  the  first  had  given  or 
was  about  to  give.  It  could  be  a case  of  concurrence, 
and  have  the  force  due  to  a concurrence  only  on  condi- 
tion, that  the  two  witnesses  had  had  no  opportunity  of 
knowing  what  each  other  had  testified,  or  were  about 
to  testify  to. 

1175.  And  so  of  circumstances ; when  one  will  ac- 
cCi?cnucZtanceaf  count  for  the  existence  of  others,  there  is  no 


III.]  METHODS  OF  PROOF  AND  REFUTATION. SECT.  V.  323 


concurrence.  It  is  merely  an  accumulation  of  circum- 
stances, and  in  fact  of  but  little  value. 

1176.  This  is  the  Method  of  Argument  upon  which, 
for  the  most  part,  the  conclusions  of  the  The  sphere  of 
Historian — that  is,  the  series  of  statements  itsuse- 
which  make  up  what  he  calls  his  history,  depend.  Such 
is  the  infirmity  of  human  testimony — man’s  liability  to 
error  in  perceiving — his  susceptibility  to  the  uncon- 
scious influences  of  prejudice  and  passion,  m History, 
and  worse  than  all  his  perverse  inclination  to  mistake 
and  misrepresent  others,  that  the  cautious  student  of 
history  will  seldom  believe  even  the  most  explicit 
testimony  of  a single  witness,  unless  there  are  other 
witnesses  or  material  circumstances  concurring  with 
his  statement.  And  if  the  influence  of  this  concur- 
rence be  against  any  man’s  testimony  clearly,  and  with 
any  very  great  force,  we  set  it  aside  with  the  charitable 
judgment  that  it  was  a mistake  of  his. 

1177.  In  the  criminal  jurisdiction  of  our  Courts 
also,  concurrence  of  testimony,  or  Circum- 
stantial Evidence,  as  it  is  called,  is  for  the  crimitia["jun?3- 
most  part  all  that  can  be  had.  The  criminal  ictl°"’ 
never  surrounds  his  acts  with  witnesses  who  can  testify 
to  his  guilt.  On  the  contrary  he  seeks  to  be  as  far 
removed  as  possible  from  such  means  of  convicting  him 
of  the  crime. 

1178.  Moreover,  as  showing  the  value  of  this  kind 
of  testimony,  there  are  some  crimes  of  which 

a man  cannot  be  convicted  on  the  testimony  superior  to  sin- 
of  a single  witness,  without  a strong  concur-  mony’m1  some 
rence  ot  circumstantial  evidence,  as  perjury  CiSes' 
for  instance  ; and  in  many  cases  concurrence  of  cir- 
cumstances is  sufficient  to  destroy  entirely  the  direct 
testimony  of  an  individual  witness. 


324 


LOGIC. PART  II. 


[CHAP. 


SECTION  VI. 


Of  Progressive  Approach. 

1179.  There  are  certain  Methods  of  Argument 
which,  while  from  their  nature  they  are  incapable  of 

occasion  for  establishing  an  absolute  certainty,  do  never- 
g?lssfwot  ap'  theless  answer  a good  practical  purpose  ; 
proacti.  and  for  certain  extraneous  reasons  are  pre- 
ferred in  some  cases  to  Methods  which  could  give  a 
different  kind  or  degree  of  certainty.  There  are  other 
cases  where  absolute  certainty  is  unattainable,  though 
we  may  make  some  approach  to  it.  All  these  Methods 
we  call  Methods  of  Progressive  Approach  •,  of  which 
there  are  several  kinds. 

1180.  (1)  A posteriori  efforts  to  prove  an  a priori 
proposition. 

1181.  Suppose  we  take  for  illustration  the  first  law 

First  case.  of  motion — ■“  A body  in  motion  will  continue 

illustration.  to  move  for  ever  unless  it  be  stopped  by 
some  force  external  to  itself.” 

This  proposition  contains  terms  and  elements  which 
can  never  be  justified  by  any  a, posteriori  Method.  In 
the  first  place  we  can  never  remove  all  the 
proof posSe-  external  forces  that  act  upon  any  body,  so  as 
terms  of  tile  to  see  it  in  motion  uninfluenced  by  any  thing 
i roposition.  external  to  itself.  Always  there  will  be  some 
friction,  some  resistance  of  the  atmosphere,  &c.  But 
in  the  second  place  if  we  could  fulfil  this  condition,  an 
observation  or  experiment  could  never  extend  through 
the  time  implied  in  the  Proposition  to  be  proved,  “for 
ever.”  We  might,  if  the  first  condition  was  fulfilled,  see 
it  move  a long  time — but  “for  ever”  is  not  only  some- 
what longer  than  any  individual  observer  will  live  to 
test  the  matter;  but,  even  if  that  difficulty  could  be 
satisfactorily  disposed  of,  the  proof  of  the  proposition 
by  this  method  could  not  be  completed  until  it  would, 
be  too  late  to  be  of  any  practical  utility. 


HI.]  METHODS  OF  PROOF  AND  REFUTATION. SECT.  VI.  325 


1182.  Our  only  resource,  therefore,  is  to  approach 
the  conditions  as  nearly  as  possible.  We  We  can  only 
set  a body  in  motion  with  a given  amount  ™'oxp™wnon 
of  friction  and  retarding  forces — it  goes  a means- 
certain  length  of  time.  We  start  the  same  body,  or 
another  precisely  like  it,  with  less  of  friction,  and  it 
keeps  moving  much  longer ; and  the  less  there  is  to 
retard  it,  the  longer  it  moves — -and  we  infer  that  if  it 
had  nothing  to  retard  it  it  would  move  for  ever. 

1183.  The  Proposition  can  he  proved  a priori  from 
the  property  of  inertia,  which  is  contained  in  It  may  be  0e. 
the  class-conception  of  Matter  as  a material  monstrated- 
property. 

1184.  But  a posteriori  we  can  prove  only  general 
truths,  with  the  possibility  of  exceptions  to 

, ,i  i . Absolute  truths 

them,  while  the  absolute  certainty  ot  um-  proved  only  by 

\ . . n -i  ,•  Demonstration. 

versa!  truths,  which  admit  no  exceptions, 
can  be  proved  only  a priori  by  Demonstration. 

1185.  (2)  A second  modification  of  this  Method  is 
afforded  in  the  mathematical  doctrine  of  The  D(?ctrine 
limits.  That  is,  “Whatever  is  true  of  any  progre^ve  AP* 
point  indefinitely  near  to  any  limit,  is  true  proach- 

at  that  limit.” 

1186.  Thus  if  we  have  the  question  of  the  quadra- 
ture of  the  circle,  What  is  the  ratio  of  the 
diameter  to  the  circumference  ? We  can  ture  of  the  Ch- 
answer  only  by  Progressive  Approach.  We 

can  construct  a polygon  within  the  circle,  whose  sides 
are  near  to  the  circumference  of  the  circles,  but  not 
coincident  with  it.  We  may  then  bisect  the  sides  of  that 
polygon,  and  so  on,  but  the  polygon  can  never  become  a 
circle.  It  can  only  approach  it  indefinitely  near.  So, 
too,  the  number  that  expresses  the  ratio  of  the  radius  to 
the  circumference  becomes  a decimal  3.141,  and  extend- 
ing indefinitely,  but  it  can  never  become  complete. 

1187.  Arguments  from  the  force  of  Terms,  from 

Testimony,  from  Concurrence,  from  Circum-  cumulative 
stances,  in  fact  Cumulative  Arguments,  and 
Probable  Arguments  of  all  kinds,  are  but  Ap' 


326 


LOGIC. — PAHT  II. 


[CHAP. 


Progressive  Approaches  towards  the  absolute  certainty 
of  the  truth  of  the  Proposition  which  they  aim  to 
establish.  A jury  in  criminal  cases,  for  instance,  is 
bound  not  to  convict  a criminal  so  long  as  there  is  a 
reasonable  doubt  left  of  his  guilt.  And  yet  the  records 
of  criminal  jurisdiction  furnish  many  instances  in  which 
persons  have  been  convicted,  who  were  afterwards 
found  to  have  been  entirely  innocent. 

1188.  In  speaking  of  Arguments  of  this  kind  as 
progressive  ap-  but  Progressive  Approaches  to  certainty,  we 
to^than^D0"  iruist  be  understood  to  refer  to  their  Logical 
monstrative.  character  rather  than  to  their  practical  effect, 
in  point  of  fact  the  mass  of  minds  are  sooner  and  easier 
persuaded  by  a Progressive  Approach  than  by  a De- 
monstration, even  in  those  cases  where  a Demonstration 
is  possible.  It  requires  a peculiar  mental  constitution, 
or  at  least  much  practice,  to  be  so  familiar  with  the 
Method  of  Demonstration  as  to  be  fully  under  the  in- 
fluence of  its  power. 

1189.  And  on  the  other  hand,  minds  which  are 
particularly  accustomed  to  the  Methods  of  Demonstra- 
te,. of  do-  tionj  or  which  are  constitutionally  peculiarly 
gress!ving  ap-  susceptible  to  its  force,  not  unfrequently  ac- 
proach.  quire  a contempt  for  what  is  called  moral 
reasoning,  and  a distrust  of  its  conclusive  force,  which 
iS  entirely  unjustifiable.  And  it  is,  perhaps,  one  of 
the  most  difficult  branches  of  practical  Ethics,  to  deter- 
mine where  the  force  of  a Progressive  Approach  be- 
comes a sufficient  ground  for  the  responsibility  of 
action. 

SECTION  VII. 

Of  the  Argumentum  ad  Ignorantiam. 

1190.  This  Argument  consists  in  proving  that  a 
Argumentum  given  Proposition  is  true,  because  we  know 

tium.  lenoran"  of  no  reason  why  it  should  not  be  true,  or 
why  the  truth  should  be  otherwise. 


III.]  METHODS  OF  PROOF  AND  REFUTATION. SECT.  VII.  327 

1191.  An  instance  of  this  occurs  where  we  should 
least  of  all  expect  it,  in  Herschel’s  Discourse  on  the 
Study  of  Natural  Philosophy.  He  says  that  illustration, 
on  the  old  principle,  “ that  Nature  abhors  a vacuum,” 
as  accounting  for  the  rising  of  the  mercury  in  a Baro- 
meter, and  such  like  phenomena,  “We  know  of  no 
reason  why  Nature  should  not  abhor  the  vacuum  as 
much  on  a high  mountain  as  in  the  plain  below.” 
Therefore  the  Barometer  ought  to  stand  as  high  on  a 
mountain  as  in  the  plain  below.  This  of  course  as- 
sumes that  if  there  was  any  reason  for  its  being  other- 
wise, he  or  we  should  know  it ; or  which  is  the  same 
thing,  that  we  know  all  the  reasons  for  whatever  phe- 
nomena may  come  before  our  minds. 

1192.  Now  there  are  undoubtedly  cases  in  which 
one’s  ignorance  of  any  fact  or  phenomena,  ^ f 
is  a presumption  at  least  of  its  non-existence,  fact"  or  princi- 
Thus  an  alleged  fact  in  any  science  of  which 

none  of  those  most  familiar  with  the  science  no,1'reaitJ' 
had  any  knowledge,  would  be  looked  upon  with  great 
suspicion.  And  so  universally  just  in  proportion  to 
one’s  opportunity  to  know,  is  his  ignorance  a ground 
or  principle  of  proof  of  the  non-reality  of  the  alleged 
fact. 

1193.  The  Ad  Ignorantiam  labors  not  only  under 
the  disadvantages  of  Negative  Testimony,  and  of  Posi- 
tive Testimony  to  a Negative  Proposition  (858-863), 
but  also  under  peculiar  disadvantages  of  its 

-n  i i , t ° . Value  increases 

own.  _b  or  what  man  adequately  conceives  with  our  know- 
and  knows,  is  an  indefinitely  small  amount  e se' 
when  compared  to  the  infinitum  of  the  knowable  ; and 
the  value  of  the  Argumentum  ad  Ignorantiam  increases 
from  nothing  up  towards  certainty,  only  as  our  know- 
ledge advances  from  total  ignorance  up  towards  omnis- 
cience. 

1194.  There  are  some  cases,  however,  in  which  this 
element  enters  pretty  largely  into  our  Methods  of  In- 
vestigation and  Argument.  In  investigating  Use  in  investi. 
Causes,  for  instance,  both  Final  and  Efficient,  gatins  Causes- 


328 


LOGIC. PART  II. 


[chap. 


so  strong  is  the  belief  in  their  reality,  that  we  often 
affirm  the  causality  of  a particular  Antecedent  or  Mode, 
not  because  we  can  see  any  connection  between  the 
facts,  but  simply  because  we  can  see  no  other  fact  of 
which  to  affirm  it.  We  can  see  no  connection,  for 
instance,  between  the  resin  and  the  kind  of  electricity 
that  it  excites.  But  Induction  having  established  the 
invariable  antecedence,  we  affirm  a causality  simply 
because  we  believe  that  there  is  a cause,  and  we  do 
not  know  of  any  thing  else  that  could  have  produced 
the  observed  phenomena,  except  the  resinous  sub- 
stances. 

1195.  Such  reasoning  can  hardly  be  said  to  be 
based  upon  any  general  principle  which  comprehends 

want  of  prin-  the  facts  of  the  case  ; or  in  more  exact  terms, 
ciple-  any  principle,  the  statement  of  which  fur- 

nishes a Middle  Term,  as  a means  of  proving  the  Pre- 
dicate of  the  Subject  in  the  Conclusion. 

SECTION  VIII. 

Of  Refutation. 

1196.  Refutation  supposes  a foregoing  proposition 
already  asserted  or  assented  to,  which  it  is  desirable 

to  disprove.  As  this  foregoing  proposition 

Refutation  sup- 

poses  a conrju-  can  hardly  be  an  axiom  or  intuitive  uidg- 
going  Argu-  merit,  it  must  be  regarded  as  a conclusion 
to  a course  of  reasoning,  or  at  least  as  resting 
on  Premises  or  grounds,  which  must  in  some  way  be 
removed  before  we  can  expect  those  who  have  adopted 
the  conclusion  to  give  it  up,  or  justify  ourselves  in 
dissenting  from  it. 

1197.  In  cases  where  there  has  been  an  Ignoratio 
Elenchi , or  the  proof  of  a Proposition  which  is  not 

gnoratio  a Re-  to  the  purpose,  we  have  no  occasion  to  show 
futation.  that  the  conclusion  is  untrue,  by  any  method. 
It  is  enough  to  show  that  it  is  not  to  the  purpose.  This 
is  not  in  fact  so  much  a refutation  of  the  Argument  or 


m.]  METHODS  OF  PROOF  AND  REFUTATION. — SECT.  IX.  329 

Conclusion,  as  the  rescuing  our  cause  from  the  effects 
of  a false  and  improper  attack. 

1198.  Setting  this  case  aside,  therefore,  as  not 
strictly  belonging  to  Methods  of  Refutation,  we  may 
divide  all  our  Methods  into  three  classes  : — Three  Methods. 
(1)  the  Direct ; (2)  the  Indirect ; (3)  Personal  Refuta- 
tions. 


SECTION  IX. 

Of  Direct  Refutation. 

1199.  The  first  form  of  Direct  Refutation  to  he  con- 
sidered, is  that  in  which  we  prove  the  contra-  First  Method, 
dictory  of  the  Proposition , which  may  have  been  af- 
firmed without  regard  to  any  Premises  or  means  of 
Proof  which  may  have  been  given  to  prove  its  truth. 

1200.  Mo  Proposition  and  its  contradictory  can  be 
true  at  the  same  time.  If  now  we  have  any  universal  pro- 
Universal  Proposition  asserted,  we  can  refute  ^‘‘by  e/mp- 
it  directly  if  we  can  find  what  is  called  an  tions- 
Exception — that  is,  a fact  included  in  the  sphere  of  its 
Subject,  with  which  the  Predicate  of  the  Proposition 
cannot  he  connected  by  a Copula  in  the  same  quality 
as  in  the  original  Proposition.  If  that  Proposition  was 
affirmative,  its  Predicate  must  be  denied  of  the  Excep- 
tion ; or  if  negative,  it  must  be  affirmed  of  it.  Thus 
if  I say  that  all  the  men  in  a given  company  are  sit- 
ting down,  the  Proposition  would  be  refuted  if  one 
could  show-that  there  was  so  much  as  one  exception, 
one  individual  that  was  not  sitting  down. 

1201.  The  mere  inability  to  affirm  the  Predicate 
could  hardly  be  regarded  as  a refutation.  a caution. 
It  would  be  a piece  of  mere  negative  testimony  (see  860). 

1202.  In  all . such  cases  the  appeal  is  always  to 
some  of  the  primary  means  of  investigation,  Exceptions 
which,  because  they  are  primary,  are  both  how  p^'-ed. 
investigation  and  proof  (1040). 

1203.  We  must  remember  that  Individual  judgments 
always  precede  Universal  or  General  judgments,  and 


330 


LOGIC. — PABT  II. 


[CHAP. 


that  general  judgments  are  based  upon  the  individual.* 
And  by  no  principle  can  the  general  judg- 

Individual  \ 1 1 . . .V5  ,-i  i 

judgments  first  ment  be  made  more  certain,  than  the  least 

and  surest.  . • p , i •-!••-»  ■ 

certain  ot  the  individual  judgments  compre- 
hended in  it ; as  the  chain  can  never  be  any  stronger 
than  its  weakest  link.  Hence  the  assertion  of  an 
exception  to  any  Universal  Proposition  is  but  an  ap- 
peal to  the  primary  judgments  ; and  of  course,  there- 
fore, it  must  have  a greater  degree  of  certainty  than 
the  Universal  Proposition  itself. 

1201.  An  Exception,  however,  never  refutes  a 
Exceptions  do  mere  general  Proposition,  since  in  all  con- 

not  refute  Ge-  . . • , • • i • • -> 

nerai  Proposi-  tmgent  matter  it  is  a recognized  principle 
universal.  only  that  all  suck  admit  of  exceptions.  “ Excep- 
tio  probat  regulam ,”  has  come  to  be  an  axiom. f But 
an  Exception  is  a refutation  to  a Universal  Proposition. 
It  destroys  its  Universality,  and  therefore  its  Formal 
character.  Of  course  it  is  immaterial  whether  the 
Proposition  was  affirmative  or  negative,  so  far  as  the 
effect  of  the  Exception  is  concerned. 

1205.  But  if  the  Proposition  to  be  refuted  be  Par- 
Refutation  of  ticular  rather  than  Universal,  then  of  course 
proposition.1'111"  it  can  be  refuted  only  by  the  Proof  of  its 
contradictory  Universal.  And  this  can  be  proved  in 
one  of  two  ways  only  : (1)  first  by  an  a priori  demon- 
stration in  necessary  matter ; or  (2)  by  an  actual  in- 
spection of  all  the  individuals  included  in  the  sphere 
of  the  Logical  Whole  ; a part  of  which  constitutes  the 
subject  of  the  Particular  judgment  which -we  wish  to 
refute. :[ 

* The  Individual  judgment  is  always  first  in  point  of  time,  and  if  we 
proceed  from  that  hy  Induction  we  get  a General  judgment ; but  if  we 
evolve  the  Predicate  from  the  necessary  matter  of  the  conception  of  the 
subject,  our  judgment  becomes  a Necessary  one. 

f Of  course  it  is  not  the  Exception  that  proves  the  rale,  strictly  speak- 
ing : hut  the  fact  that  it  has  been  noticed  as  an  exception , proves  that  the 
general  Proposition,  to  which  it  is  contradictory,  has  been  recognized  as  a 
rule  which  is  true  in  general. 

{ In  the  first  case  we  obtain  a judgment,  which  is  Universal,  ex  neces- 
sitate rei ; in  the  second  it  is  only  Universal,  de  facto — as  in  fact  there  is  no 
necessity  that  it  should  be  so  or  always  remain  so. 


m.]  METHODS  OF  PROOF  AND  REFUTATION. SECT.  IX.  331 


Second  Me- 
thod of  Direct 
Refutation. 


1206.  But  there  may  he  many  cases  in  which  nei- 
ther of  these  modes  of  direct  refutation  are  Refutation  of 
practicable,  where  we  can  have  no  a priori  not 
demonstration — nor  yet  submit  the  indivi-  slble- 
duals  included  within  the  sphere  of  the  subject  to  the 
test  of  observation  arid  experiment. 

1207.  In  all  such  cases  we  may  release  ourselves 
from  the  obligation  to  assent  to  a Conclusion 
lyy  ref  uting  the  Reasoning.  This  we  accom- 
plish not  by  disproving  the  Conclusion,  but 
by  showing  that  it  is  not  proved  by  the  Premises  ; we 
show  in  fact  from  the  Premises  themselves  without 
referring  to  any  matter  not  contained  in  them,  that  the 
Conclusion  is  invalid,  and  ought  not  to  have  been 
drawn  from  those  Premises.  It  may  be  true  as  a Pro- 
position, but  is  not  proved  as  a Conclusion. 

1208.  This  may  be  done  in  four  ways : (1)  in  the 
first  place  we  may  have  a simple  Non  sequi-  Non  sequitur. 
tur , as  in  all  cases  of  Fault  or  Fallacy  in  Form.  In 
this  case  the  Premise  may  be  true  and  the  Conclusion 
true,  and  yet  no  connection  between  them  ; or  the 
Premise  may  be  true  and  the  Conclusion  false.  Thus 
if  any  of  the  five  Canons  (177)  be  violated,  we  have  a 
simple  Non  sequitur. 

1209.  So,  also,  if  in  Conditionals  we  deny  the  Ante- 
cedent to  destroy  the  Consequent  (682),  or  Non  sequitur 
from  the  denial  of  the  Consequent  infer  the  kT uc on d isfu nc - 
contrary  and  not  the  contradictory  merely  tives- 

of  the  Antecedent.  Or  if  in  Disjunctives,  we  apply 
the  Modus  ponente  tollens  (710),  where  the  excluded 
Middle  is  produced  by  the  opposition  of  alternate 
rather  than  coordinate  species  or  parts.  In  short  any 
Fault  or  Fallacy  in  Form  will  give  a Non  sequitur. 
Hence  it  is  always  a sufficient  refutation  to  point  out 
such  a fault. 

1210.  (2)  In  the  second  place  we  may  have  a Sequi- 
tur per  Fallaciam — using  the  word  F allacy  in  seqmter 
its  strictest  sense — as  indicating  some  decep- 

tive  use  of  a Formula,  where  the  Premises,  each  taken 


332 


LOGIC. — PART  II. 


[CHAP. 


by  itself  is  true,  and  the  conditions  and  require- 
ments of  the  Formula  are  fulfilled.  Of  these  it  will  be 
seen  (Part  I.  Chap.  IY.  Sec.  3,)  that  there  are  five  : 
(1)  Ambiguous  Middle;  (2)  Division;  (3)  Composi- 
tion ; (4)  Accidents  ; (5)  Quid. 

1211.  Any  one  of  these  Fallacies  of  course  destroys 
the  validity  of  an  Argument ; and  although  the  Con- 
i The  nconciu.  elusion  may  still  be  true,  we  are  no  longer 
true^  notwith-  bound  to  receive  it  as  a Conclusion  after 
Fallacy f e such  a Fallacy  has  been  pointed  out  in  the 
process  by  which  one  has  arrived  at  it. 

1212.  (3)  In  the  third  case  we  may  have  a Sequitur 
per  non  veram , in  which  case  there  is  neither  fault  in 

sequitur  Pcr  F omi  nor  Fallacy  in  the  use  of  matter,  but 
non  veram.  simply  the  assumption  of  Premises,  one  or 
more  of  which  are  not  true. 

1213.  This  will  be  seen  occurs  in  the  case  of  Non 
causa  pro  causa , as  stated  in  Part  I.  (738),  together 

cases  of  Pen-  with  the  assumption  of  Sequence  where  there 
tto  Pnncipii.  js  none?  non-exclusion  .of  Middle,  &c.,  &c. 
In  all  these  cases  a Proposition  is  assumed  as  true, 
which  is  not  so.  And  whether  it  be  expressly  stated 
or  inqfiied  as  the  suppressed  Premise  of  an  Enthy- 
meme,  the  Sequence  of  a Conditional,  &c.,  it  is  equally 
mischievous;  and  needs  to  be  distinctly  evolved  if  it 
were  not  expressly  stated. 

1214.  It  thus  becomes  a Proposition,  which  we  shall 
The  False  pre-  need  to  disprove — unless  its  falsity  be  ob- 
disproof.  vious  witnout  any  proof.  I Ins  can  be  clone 
of  course  only  by  proving  the  contradictory  of  the  False 
Pi  ■emise. 

1215.  (4)  But  finally,  we  may  have  a Fault  in  Me- 
thod, or  a misapplication  of  Method  to  Matter ; as  if 

Fault  in  Me-  we  should  attempt  to  apply  Demonstration 
thod.  to  contingent  matter,  and  determine  realities 

in  being  from  our  conceptions,  stated  as  definitions. 
This  was  the  great  fault  that  prevailed  among  the 
students  of  the  Natural  Sciences  from  Aristotle  down 
to  Bacon. 


HI.]  METHODS  OF  PROOF  ASD  REFUTATION. — SECT.  X.  333 

1216.  But  in  modern  times  we  have  a tendency  to 
the  opposite  error.  One  writer*  has  attempted  to  ap- 
ply Induction  to  the  religious  history  of  the  voiney’s  Fault, 
world,  and  to  prove  the  falsity  of  Christianity  from  the 
fact,  that  all  religions  except  that  contained  in  the 
Scriptures  have  been  delusions. 

SECTION  X. 

Of  Indirect  Refutation. 

1217.  This  consists  in  proving  a Proposition  untrue, 

by  showing  that  it  contains  or  comprehends  Indirect  Retu- 
that.  which  is  false.  tat,on- 

1218.  In  the  first  place  we  may  show  a Proposition 
to  be  false  by  evolving  from  it,  by  Immediate  By  jmme(iiate 
Inference , an  untruth.  Thus,  one  writer  says  Interence-. 
that  the  human  souls  are  propagated  by  “ decision  ; ” 
and  the  context  shows  that  by  “ decision  ” he  means 
the  cutting  off  of  a part.  But  “ decision  ” or  division 
implies  extension,  and  extension  is  a property  of  mat- 
ter and  not  of  spirit. 

1219.  In  the  second  place  we  may  refute  one’s 
reasoning  by  what  is  called  the  Reductio  ad 
Absuraum.  in  tins  process  we  introduce  a Reductio  ad 
other  matter,  which  is  either  ‘admitted  as 

true,  or  which  admits  of  proof  beyond  further  cpiestion, 
and  combines  this  new  matter  with  that  part  of  which 
was  given  before,  which  we  wish  to  show  to  be  false. 

1220.  This  Method  is  often  spoken  of  as  the  process 
of  showing  that  one’s  “ Principles  ” or  “ argu-  Pop„iar  names 
ment  proves  too  much.”  Thus  the  infidel’s  forlhe Method, 
argument,  that  the  apparent  death  of  the  body  implies 
the  death  of  the  soul  and  the  cessation  of  existence,  as 
Bishop  Butler  shows  in  his  Analogy,  “ proves  too 
much.”  It  proves  that  the  larvse  of  the  Metabolians 
die  when  they  go  into  the  chrysalis  state  ; whereas 


See  Voiney’s  Ruins,  or  Meditations  among  the  Ruins  of  Empires. 


334  LOGIC. — PAKT  n.  [chap. 

they  do  not  die  but  only  change  their  mode  of  exist- 
ence. 

1221.  Now  if  any  general  Proposition,  that  is,  a 
Proposition  with  a general  term  for  a subject  he  true, 

Fundamental  its  Predicate  must  he  true  of  every  species 
Fndirect6  Reiin  included  in  the  genus  denoted  by  the  sub- 
tation.  ject.  If  then  we  can  discover  a species,  of 
which  the  subject  of  that  general  Proposition  can  be 
predicated,  while  its  Predicate  cannot,  the  general 
Proposition  itself  must  be  untrue. 

1222.  Thus  to  recur  to  Bishop  Butler’s  argument 
illustration.  again.  The  infidel  had  asserted  that  the  soul 
dies  with  the  body — fihe  assertion  was  based  on  the 
appearance  of  death — and  hence  implied  the  Major 
Premise,  that  “ in  all  cases  of  an  apparent  death  of  the 
body,  there  is  a total  cessation  of  the  existence  of  the 
individual.” — Using  this  Major  Premise,  we  may  com- 
plete the  Formula  thus  : 

Whenever  the  body  dies  there  is  a termination  of 
the  individual  existence. 

The  body  dies  in  what  we  call  the  death  of  man. 

.•.  In  what  we  call  the  death  of  man  there  is  a ter- 
mination of  the  individual  existence. 

But  says  Bishop  Butler  there  is  a death  of  the  body 
in  the  larvae  of  Metabolian  insects.  Using  this  for  a 
Minor  Premise  to  the  .Major  Premise  just  given,  and 
we  have  for  Conclusion  : 

.*.  There  is  a termination  of  the  individual  existence 
of  each  Metabolian  when  it  goes  into  the  chrysalis 
state. 

This  Conclusion,  however,  is  confessedly  untrue, 
and  yet  the  Major  Premise  is  the  same  as  the  infidel 
had  used  ; the  Minor  Premise  is  indeed  different,  but 
then  it  is  a Proposition  that  no  one  can  dispute.  Hence 
the  Major  Premise,  common  to  both  Conclusions,  must 
be  untrue. 

1223.  By  this  we  do  not  mean  to  say  that  the  Pro- 

The  disproved  position  had  no  element  of  truth  in  it,  or 
! b0  that  this  Reductio  has  shown  that  the  Predi- 


1H.]  METHODS  OF  PROOF  AND  REFUTATION. SECT.  X.  335 

cate  is  not  true  of  any  individuals  included  in  the  sub- 
ject ; but  only  that  inasmuch  as  the  Proposition  is  not 
true  of  all,  we  cannot  admit  it  to  be  true  of  any,  until 
it  is  modified  by  some  modal  which  shall  give  either 
the  Differentia  of  an  included  species  of  which  it  may 
always  be  affirmed,  or  expressive  of  a term  or  a condi- 
tion in  which  it  may  be  affirmed  of  any  one  of  them 
generally.  And  until  this  has  been  done  by  the  infidel 
the  refutation  is  complete, 

1221.  The  Indirect  Methods  of  Disproof  as  well  as 
the  Indirect  Method  of  Proof  imply  that  there  Indirect  Me- 
is  more  than  one  way  of  knowing  the  truth  aao!Vect 
of  the  Proposition  which  it  is  sought  to  dis-  “od  C‘°nct11j: 
prove.  Otherwise  there  would  he  no  means  sion- 
of  disproving.  Thus,  as  we  have  seen,  we  may  dis- 
prove a Proposition  by  proving  directly  its  contra- 
dictory. This  gives  us  two  methods  to  the  same  Pro-, 
position,  since  from  any  Proposition  to  its  contradictory 
is  an  immediate  inference. 

1225.  Or  again,  we  may  disprove  a Proposition  as 
a Premise  by  the  reductio  ad  ahsurdum. 

But  this  implies  that  we  have  some  other  the  Reductio 

•S  T n • , i -l  • ad  Absurdum. 

means  or  method  or  proving  that  Conclusion 
or  its  contradictory,  as  the  case  may  be.  Otherwise 
we  should  not  know  which  of  the  two  Conclusions  was 
right.  We  cannot  pronounce  our  Proposition  to  be 
absurd  or  false,  until  we  have  ascertained  that  it  is 
contradictory  to  another  which  we  know  to  be  true. 
Affirmative  judgments  are  antecedent  in  point  of  time 
to  the  Negative,  and  the  test  of  a theory  or  Method  is 
that  it  gives  results  in  aocordance  with  what  we  know 
to  be  true,  independent  of  the  Method  or  theory  in  all 
those  cases  of  which  we  know  any  thing,  except  by 
means  of  the  theory  or  Method  itself. 

1226.  The  value  of  the  Method  will  of  course  de- 
pend upon  the  certainty  of  the  newly  intro-  .The  Refuta- 
duced  Premise  or  Matter,  and  of  course  is  upon  the  cer- 
worth  nothing  unless  that  Premise  be  more  new  Matter, 
certain  than  the  common  Premise  which  it  seeks  to 
redargue. 


336 


LOGIC. — PAItT  II. 


[chap. 


1227.  What  is  called  the  Argumentmn  ab  Ahsurdo 
The  Argumen-  is  merely  the  inference  from  the  Absurdity 
do.  oi  the  Conclusion,  that  one  or  the  other  ot 

the  Premises,  or  both  of  them  must  be  untrue.  This 
can  seldom  be  of  any  further  use  than  a mere  appeal 
to  prejudice,  since  one  is  not  likely  to  announce  an 
absurd  opinion  without  some  force  of  Premises  to  sup- 
port it  which  may  need  a Refutation. 


SECTION  XI. 

Of  Personal  Refutations. 

1228.  There  are  certain  Methods  of  Refutation, 
which,  while  they  have  no  conclusive  force  of  a general 
personal  Refu-  character,  are  often  of  great  rhetorical  effi- 
tahons.  ciency  in  putting  a stop  to  further  contro- 
versy. These  I have  called  Personal  Arguments. 

1229.  (1)  The  Argumentum  ad  Hominem  consists 
Ar?um.entum  in  appealing  to  a man’s  acts,  or  previous  de- 

ai  Homirnm.  clarations,  or  avowed  principles,  as  being 
inconsistent  with  the  position  he  is  at  present  main- 
taining. 

1230.  The  ad  liominem  proves  nothing  categori- 
what  it  proves,  cally.  The  ojiinion  of  the  Respondent  is  used 
as  a Premise  against  himself:  It  may  effectually  annoy 
or  even  answer  him  ; but  it  can  prove  nothing  more 
than  that  such  and  such  is  his  opinion,  or  results  from 
his  opinion.  The  Conclusion  can  have  no  more  truth 
than  the  subjective  Premise  or  personal  opinion  of  the 
person  to  whom  the  Argument  is  addressed. 

1231.  (2)  The  Argumentum  ad  Verecundiam  is  an 
Argumentum  appeal  to  the  opinion  of  an  authority  which 

diam.  Verecun'  the  person  against  whom  the  argument  is 
used  is  bound  to  respect  and  follow,  on  the  score  of 
modesty. 

1232.  This  argument  also  can  hardly  be  said  to 
ita  force.  prove  any  thing  categorically.  It  is  used 
and  very  well  serves  to  embarrass  an  antagonist. 


in.]  METHODS  OF  PROOF  AND  REFUTATION. SECT.  XI.  337 

Beyond  this  it  has  but  little  force.  It  gives  for  a Pre- 
mise the  opinion  of  the  individual  or  authority  cited, 
and  the  Conclusion  can  have  no  force  except  what 
results  from  the  respect  due  to  that  authority ; a 
force  which  may  have  far  greater  moral  than  logical 
weight. 

1233.  The  Argumentum  ad  Invidiam  as  it  is  some- 
times called,  is  really  no  argument  at  all.  Ar^umentum 
It  consists  in  appeals  to  the  passions,  preju-  ai  Invidiam- 
dices,  or  feelings  of  people,  for  the  purpose  of  exciting 
emotions  unfavorable  either  to  a cause  or  the  person  of 
him  who  advocates  it.  However  effective  this  may  be 
in  a rhetorical  point  of  view,  it  accomplishes  nothing 
logically  ; and  proves,  if  it  proves  any  thing,  only  that 
those  who  resort  to  this  mode  of  argument  are  better 
skilled  in  Rhetoric  than  in  reasoning,  and  know  more 
of  the  Formulae  of  Billingsgate  than  of  Logic. 


338 


LOGIC. — PART  II. 


[chap. 


CHAPTER  IV. 


METHODS  OF  INSTRUCTION  AND  CRITICISM. 


SECTION  I. 

Classification  of  Sciences. 

1234.  It  may  not  be  inappropriate  to  give  a Classi- 
fication of  the  Branches  of  Human  Knowledge  before 
proceeding  with  the  appropriate  topics  of  this  Chapter. 
8uch  a classification  has  been  already  anticipated  in 
some  measure,  and  seems  very  generally  to  have  been 
considered  as  belonging  to  this  part  of  Philosophy. 

1235.  We  have  already  referred  to  the  early  divi- 
sion of  human  knowledge  into  three  branches  : Physics, 

Early  ciassi-  Ethics,  and  Logic  (5).  But  a slight  advance 
becomes  inade-  i"  science,  however,  rendered  this  classi- 
quate-  fication  inadequate  and  unsatisfactory.  It 

must  however  be,  to  some  extent,  the  basis  of  all  divi- 
sions. The  first  department,  Physics,  including  all 
branches  of  knowledge  that  have  for  subject-matter 
material  objects  in  the  concrete  ; Logic,  including  all 
branches  that  treat  of  the  intellect,  and  are  based  upon 
the  elements  furnished  by  it,  the  realities  of  truth,  and 
the  a priori  conceptions  ; and  Ethics,  including  all  that 
relate  to  man  as  having  a destiny  to  accomplish,  im- 
plying society,  religion,  and  the  state  with  its  institu- 
tions and  vested  rights,  as  of  Property,  &c.,  as  a means 
of  accomplishing  that  destiny. 


XV.]  METHODS  OF  INSTRUCTION  AND  CRITICISM. SECT.  I.  339 


1236.  It  would  not  be  worth  the  while  to  follow 
the  history  of  these  classifications  minutely  if  we  had 
time.  One  or  two  of  the  classifications,  how-  Aristotle’s 
ever,  it  may  he  well  to  notice.  Aristotle  classification, 
divided  all  knowledge  in  the  first  place  into  two  coordi- 
nate parts,  the  Immediate , in  which  we  learn  every  thing 
in  particulars  and  each  by  itself  (to.  hclA  e/cacrra),  and 
the  Mediate , in  which  we  acquire  a knowledge  of  univer- 
sal (ra  naA  oXov).  From  the  Immediate  in  his  theory, 
we  deduce  by  means  of  Logic  the  knowledge  of  the 
Mediate.  Hence  Logic  is  the  instrument  or  organ  of 
all  science,  so  far  as  its  form  is  concerned.  With 
another  view  he  divided  all  knowledge  into  Philosophy 
and  History.  Philosophy  he  divided  into  Speculative 
and  Practical.  The  Speculative  becomes  Physics  or 
Mathematics , or  what  is  afterwards  called  Metaphysics, 
according  as  it  advances  in  abstraction  ; and  relatively 
to  its  end , it  is  divided  into  Physics,  Cosmology,  Psycho- 
logy, and  Theology.  Practical  Philosophy  includes 
Ethics,  Politics,  and  Economy. 

1237.  In  the  Scholastic  Philosophy  of  the  Middle 

Ages  we  have  the  division  into  the  Trivium  and  the 
Quadrivium  ; the  first  including  Grammar , scholastic 

Rhetoric , and  Logic  / and  the  lattet  includ-  classification, 
ing  Arithmetic,  Music,  Geometry,  and  Astronomy . 
They  were  described  in  these  mnemonic  lines  : 

“ Gram,  loquitur  ; Dia.  verba  docet ; Rhe.  verba  ministrat ; 

Mus.  canit ; A r.  numerat ; Ge.  ponderat ; As.  colit  astra.” 

1238.  These  seven  sciences  constituted  what  in  the 
University  distribution  was  called  the  Faculty  of  Arts. 
And  besides  these  were  three  others  : Divi- 

nit/./,  Law,  and  Medicine.  The  first  is  tribution  of  the 

^ 7 7 . it  i.  Faculties. 

regarded,  as  including  whatever  concerns 
Religion  and  its  duties  ; the  second  whatever  relates  to 
the  State  and  its  administration  of  affairs ; and  the 
third  was  understood  to  include  the  Physical  Sciences 
generally. 

1239.  Bacon  proposed  a new  classification,  dividing 


340 


LOGIC. — PART  II. 


[chap. 


all  Sciences  into  three  classes,  as  they  refer  to  either 
Memory , Imagination , or  Reason.  But  this  resulted 
Bacon's  ciassi-  in  great  confusiou,  as  there  is  scarcely  any 
fication.  branch  of  knowledge  in  which  all  these 
faculties  are  not  called  into  use  ; and  as  has  been  re- 
marked, “ his  classification  would  put  Boswell’s  Life  of 
Johnson  in  the  same  class  with  the  labors  of  Cuvier, 
and  the  researches  of  Hunter.”  Botany  and  Zoology 
were  classed  with  Metaphysics,  and  Painting  and  Mu- 
sic among  the  “ artes  volwptuarias ,”  were  ranked  with 
Cookery  and  Cosmetics. 

1240.  Locke  gave  a much  more  sensible  classifica- 
ficaiion!3  cIassi’  ti°n?  as  follows  : 


1.  Physioa 


{Experimental 
Rational 


{Economies, 
Politics, 
Ethics. 


1 Natural  History, 

Physiology. 

Theology, 

Ontology. 

• 

( Logic, 

3.  Semeiotioa  < Rhetoric, 

( Grammar. 


1241.  Dugald  Stewart  believed  a classification  of 
the  Sciences  impossible,  at  least  in  his  day.  Coleridge 

stewart  and  attempted  it  as  a basis  for  the  Encyclopedia 
coieridge.  Metropolitana , which  was  constructed  on 

his  pian.  But  as  a confession  of  failure,  he  was  obliged 
to  give  an  “ and  so  forth  ” at  the  end  ; or  rather  a 
chapter  of  “ Miscellanies ,”  which  could  not  be  in- 
cluded in  any  part  of  his  division.  This  reminds  us 
of  the  Treatise  of  Smalgruenius,  entitled  “ Re  Omni- 
bus Rebus,”  with  a supplement,  “ Re  Quibusdam 
Aliis.” 

1242.  Ampere,  however,  elaborated  a classification 
which  is  perhaps  complete  enough.  But  it  is  too  com- 

Ampfere’a  plicated.  Coleridge  had  failed  by  so  classi- 
ciassiiication.  lying,  as  to  make  his  exceptions  too  nume- 
rous. Ampere  made  his  parts  too  numerous,  and  had 
to  create  names  and  sciences  which  were  never  before 
heard  of.  ITis  division  does  not  recognize  those  names 


m.]  METHODS  OF  INSTRUCTION  AND  CRITICISM. SECT.  I.  34:1 


and  divisions  which  are  already  in 'use.  Nor  is  there 
the  remotest  probability  that  the  progressive  develop- 
ment of  Science  will  take  the  form  and  divisions  that 
he  has  pointed  out.  He  makes  one  hundred  and 
twenty-eight  sciences  in  the  last  subdivision,  or  third 
order,  as  he  calls  it — and  thirty-two  of  the  first  order. 
He  first  divides  into  two  kingdoms  Cosmological, 
including  (1)  Mathematics •;  (2)  Physics  ; (3)  Natural 
Sciences;  (4:)  Medical  Sciences  ; — and  Noological 
Sciences,  including  (1)  Philosophies  ; (2)  Dialegma- 
tics  ; (3)  Ethnological  Sciences  ; (4:)  Political  Sciences. 

1213.  Compte  has  given  a classification  also  in  his 


and  then,  as  preceding  and  implied  in  all,  he  gives 
Mathematics  or  the  Science  of  Numbers. 

1244.  This  classification,  as  will  be  seen,  does  not 
include  many  of  those  which  have  thus  far  always  been 
regarded  as  distinct  sciences.  Nor  is  the  division  suffi- 
ciently minute  to  be  of  much  service.  His  Theory 
of  Knowledge  and  his  Philosophy  are  too  hopelessly 
bad  to  allow  of  any  useful  classification  being  based 
upon  it. 

1245.  In  the  following  classification  which  I shall 
give,  I divide  first  into  three  classes  with  A new  one 
reference  to  the  end  in  view  ; and  in  the  sub-  pr0p0ied- 
divisions  I have  followed  the  received  divisions  and 
names.  Each  class  naturally  divides  itself  into  two 
departments,  differing  in  the  first  class  both  in  the 
starting-point  and  in  the  Method.  In  the  second  class 
they  differ  in  the  starting-point  only  ; and  in  the  third 
class  the  two  departments  differ  chiefly  in  the  object 
in  view — the  one  producing  objects  of  Beauty  and  the 
other  objects  of  Utility.  The  Sciences  in  the  depart- 
ments in  the  first  class  are^jiecessary  to  those  in  the 
second  class,  and  those  in  the  second  are  necessary  to 
the  third. 


Positive  Philosophy,  as  follows  : 


Compte’s  clas- 
sification. 


II.  Organic 


S Physiology, 
\ Sociology ; 


342 


LOGIC. — PART  n. 


[chap. 


Class  I. — Theoretical, 

including  those  Sciences  the  object  of  which  is  “ to 
know” 


DEPARTMENT  I. 

Exact  Sciences * (purely  physical),  based  upon 


Primary 

Phenomena 


f in  the  Atmosphere  . 
above  the  Atmosphere 

{in  the  structure  and  Nat. 
History  of  the  Earth 
on  the  surface  of  the 
Earth  . 

in  the  analysis  and  combination  of 
the  simple  Elements 
in  the  form  and  Nat.  History  of 
Solids  on  the  Earth’s  surface  . 
in  the  structure  of  living  bodies  . 
of  the  internal  functions  of  Life 
in  the  structure  and  varieties  of 
Vegetable  Life 

in  the  varieties  and  habits  of  Ani- 
mal Life  .... 
in  the  varieties  and  migrations  of 
Men 

{as  exhibited  in  Con- 
sciousness 

in  the  external  acts  of 
man 


Meteorology. 

0 URANOGRAPHY. 

. Geology. 

. Geography. 

. Chemistry. 

. Mineralogy. 

. Anatomy. 
. Physiology. 

, Botany. 

. Zoology. 

. Ethnology. 

. Psychology. 

. History.! 


* Beginning  first  with  the  facts  of  Observation,  we  have  what  are  the 
strictly  Inductive  Sciences.  I have  called  them  the  Exact  Sciences,  in  ac- 
cordance with  the  popular  usage ; not  because  they  are  any  more  exact 
than  others,  hut  because  (if  any  reason  can  he  given)  they  depend  upon  and 
require  the  greatest  exactness  of  Observation — they  depend  upon  Observa- 
tion and  Testimony. 

f History,  properly  understood,  will  of  course  include  a knowledge  of 
ancient  Geography,  the  Languages  of  ancient  as  well  as  foreign  nations  of 
the  present  day.  It  will  also  imply  a knowledge  of  the  systems  of  religion 
and  modes  of  worship  that  have  ppvailed,  and  the  progress  that  man  haa 
made  in  the  Arts  and  Sciences,  in  Philosophy  and  Literature. 


IV.]  METHODS  OF  INSTRUCTION  AND  CRITICISM. — SECT.  I.  343 


DEPARTMENT  II. 

Pure  Sciences * (purely  metaphysical),  based  upon 


Primary 

Conceptions 


' of  unity Arithmetic. 

of  forms  in  Space  ....  Geometry. 

)f  Constant 
represent-  j Quantities  . Algebra. 
ing  1 Fluxional 

1 Quantities . Calculus. 
of  the  meeting  of  lines  and  planes 
in  a point  .....  Trigonometry. 
of  visible  representation  of  Equa- 
tions ....  Analytic  Geometry. 
of  the  combination  of  Conceptions  in 

Syllogisms Analytics. 

of  Matter  as  modifying  processes  of 

Thought Method. 

of  the  conditions  and  forms  of  Know- 
„ ledge  f Ontology.  J 


* Then  in  the  nest  place  I start  with  that  other  great  coordinate  in  all 
knowledge,  the  elements  of  thought  which  exist  nowhere  in  the  reality  of 
being,  but  which  the  Reason  itself  furnishes ; and  where  all  possible  things 
are  assumed  as  real,  or  rather  the  distinction  between  the  possible  and  the 
real  entirely  disappears.  Even  the  varieties  of  Method  are  based  rather 
upon  the  varieties  of  Matter  conceived  as  possible,  than  upon  the  results 
of  experience  in  matter,  although  as  the  two  coincide  there  is  no  necessity 
of  observing  the  distinction  in  discussing  Methods. 

f By  Ontology  we  mean  the  science  of  being,  and  it  should  include  the 
discussion  of  the  necessary  law  or  forms  of  thought  under  which  we  know 
and  believe  whatever  is  supposed  to  exist  out  of  the  individual  mind  of  the 
thinker.  It  will  thus  be  found  to  furnish  the  fundamental  and  axiomatic 
principles  of  all  the  Exact  Sciences,  and  in  fact  give  to  them  their  form  or 
their  Formal  Cause. 

f The  Sciences  in  this  Department  are  purely  instrumental  and  valu- 
able as  Means  and  Helps  to  the  construction  of  the  Materials  given  in  the 
preceding  Department  into  the  Sciences  in  the  next  two  Departments,  and 
in  applying  them  to  use  as  in  the  Departments  in  the  third  Class. 

The  six  first  named,  Arithmetic , Geometry , Algebra , Calculus,  Trigonometry, 
and  Analytic  Geometry,  constitute  the  Department  of  Mathematics  ; while 
of  the  other  three,  two,  Analytics  and  Method,  constitute  Logic  ; and  the 
three  together,-  with  one  from  the  first  Department,  Psychology,  constitute 
what  is  ordinarily  called  Metaphysics. 


LOGIC. — PART  II. 


[CHAP. 


344 


Class  II. — Practical,* 

including  Sciences  tlie  object  of  which  is  “ to  do.” 

DEPARTMENT  I. 

Mixed  Sciences  f based  upon  the  Conception  of 


Matter 

and 

Motion 


f.  v , , i on  the  Earth 

in  solid  bodies  j in  the  Heavens 

. < at  rest 

- ln  1(^U1  S | in  motion 
in  gaseous  masses 

in  bodies  as  affecting  {j£® 


. Mechanics. 

Astkonomy. 
Hydrostatics. 
Hydraulics. 
Pneumatics. 
. Acoustics. 
. Optics. 


DEPARTMENT  II. 

Ethical  Sciences  ;[  based  on  the  conception  of 


Man 

and 

Action 


f in  relation  to  the  Idea  of  the  Good  . 

I as  exercising  authority  in  temporal 

affairs  

as  under  Divine  Providence 

, . ( the  State  . 

as  under  An-  Vhe  Church  _ _ 

1011  y (a Revelation  from  God 


. . Ethics. 

Polity. 
Nat.  Religion. 
Jurisprudence. 
. Ecol.  Polity. 
. Rev.  Religion. 


* The  sciences  in  the  second  class  are  those  which  develope  and  state 
the  laws  of  motion  and  of  action.  I have  called  them  Practical  because  their 
End  is  Action  ; they  all  assume  more  or  less  of  the  results  of  the  Theoreti- 
cal, or  sciences  included  in  the  first  class.  They  proceed  from  the  results 
there  obtained  by  demonstration  to  the  evolution  of  rules  or  laws. 

f These  sciences  I have  called  Mixed,  since  although  the  laws  of  Mat- 
ter are  determined  from  the  conception  of  its  nature  and  constitution  alone, 
yet  the  law  itself  is  in  point  of  fact  for  the  most  part  first  ascertained  by 
observation.  But  it  is  soon  found  to  be  implied  in  our  conceptions,  (1)  of 
Matter  (as  opposed  to  Mind)  ; (2)  of  Force  (as  opposed  to  Motive)  ; and 
(3)  of  Motion  (as  opposed  to  Thought). 

% In  the  second  Department  we  consider  the  laws  which  man  ought  to 
obey.  These  are  derived  from  a consideration  of  man  as  he  is  (Psychology 
and  Physiology),  and  of  the  destiny,  which,  by  his  voluntary  activity,  lie 
ought  to  attain.  But  as  this  destiny  implies  as  a means  of  its  accomplish- 
ment Society  or  the  Family,  and  the  State,  that  is,  a society  having  sov- 
ereignty over  individual  men,  and  a Providence  or  Moral  Governor  of  tho 


IV.]  METHODS  OF  INSTRUCTION  AND  CRITICISM. SECT.  I.  345 


Class  III. — Productive,* 

including  tlie  Sciences  the  object  of  which  is  “ to  create .” 


department  i. 


The  Fine  Arts  f or  Sciences  which  guide  the  expen- 
diture of  labor,  directed  to  the  production  of 


' in  the  Soil  . 
in  the  construction  of  Edifices  . 
in  solid  representations  of  Life 
The  Beautiful  in  perspective  representations  by 
Color  . 

in  the  combination  of  Sounds  . 

_ in  the  use  of  Language 


. Gardening. 
Architecture. 
. Sculpture. 

. Painting. 
. . Music. 

. Poetry. 


world,  to  whom  man  is  accountable,  and  whose  final  approbation  is  an 
essential  part  of  his  destiny,  we  evolve  by  Analysis  and  Demonstration  from 
these  conceptions  Society,  State,  and  Providence — the  rules  which  man 
ought  to  obey.  Hence  Ethics,  Polity,  and  Natural  Religion,  are  based  upon 
Reason  alone.  And  the  realization  of  Religion  implies  a Church  having 
authority  in  matters  of  faith.  Hence  we  have,  besides  the.  authority  of  God 
over  us,  the  two  others,  State  and  Church,  which  we  find  that  He  has 
recognized  and  sanctioned  as  guides  and  authority,  each  within  its  appro- 
priate sphere,  and  we  have  both  Jurisprudence  and  Ecclesiastical  Polity  as 
rules  of  action  within  certain  limits. 

* In  the  third  class  I have  included  all  those  sciences  the  end  of  which 
is  to  aid  man  in  the  accomplishment  of  results  out  of  himself,  and  have 
divided  them  into  two  classes,  the  Beautiful  and  the  Useful.  The  Subjects 
included  in  this  Class  are  more  commonly  called  Arts  than  Sciences.  They 
are,  however,  Sciences  of  the  Arts  ; that  is,  branches  of  knowledge  which  teach 
how  to  produce  results,  the  production  of  which  is  called  Art.  Art  is  dis- 
tinguished from  mere  Instinct  by  this  fact — namely,  that  it  is  guided  by  a 
scientific  comprehension  of  its  principles  and  processes,  whereas  Instinct  has 
no  such  comprehension. 

t I have  not  regarded  the  Methods  of  ^Esthetics  as  properly  coming 
within  the  province  of  Logic.  They  are  determined  rather  by  the  Suscep- 
tibility than  the  Reason.  Their  ultimate  Facts  are  only  experimental ; we 
can  only  refer  to  the  fact  that  a beautiful  object  does  excite  the  Emotions, 
which  we  call  the  emotions  of  Beauty  ; and  we  judge  an  object  to  be  beau- 
tiful because  it  does  excite  such  emotions.  We  cannot  prove  that  it  ought 
to  do  so.  We  can  discover  no  necessity  in  the  nature  of  the  case  for  its 
exciting  such  emotions.  Its  judgments  in  fact  are  all  Relative,  while  Logic 
deals  with  the  Absolute  alone. 


15* 


346 


LOGIC. — PART  II. 


[chap. 


DEPARTMENT  II. 


Useful  Arts’*  or  Sciences  which  guide  the  expen- 
diture of  labor,  directed  to  the  production  of 


The  Useful 


the  products 
of  mind 


in  the  Soil Agriculture. 

in  objects  beneath  the  Soil  . . Metallurgy. 

in  the  manufacture  of  the  raw  ma- 
terial   Technology. 

i . 'i  [ written  Lan- 

in nm  ip  ying  | eXpresse(jJ  guage  . Typography. 

in  1 works  of  the 

[ Fine  Arts-.  Engraving. 
in  the  increase  of  value  by  Ex- 
change   Commerce. 

in  the  promotion  of  Health  . . Medicine. 

in  the  expression  of  thought  by 

Language Khetorio. 

in  promoting  pecuniary  prosperity  . Polit.  Economy. 
in  promoting  the  National  Defence  . . War. 


1246.  Of  course  all  the  above-named  or  described 
Sciences  admit  of  being  greatly  subdivided.  In  fact 
Each  science  an}r  author  has  the  right  to  take  any  part  of 
-fables6  admit6  any  one  Science  and  treat  it  as  a Science  by 
for  subdivision,  itself,  if  he  chooses  to  do  so.  This  is,  in  fact, 
making  a subdivision  of  some  part  of  the  division  of 
Science  as  it  previously  existed.  In  this  way  the 
names  on  our  Catalogue  of  Sciences  become  more 
numerous,  and  may  in  fact  extend  beyond  any  known 
or  conceivable  limit.  I have  not  thought  it  worth 
while,  however,  to  follow  the  subdivisions  already 
made,  any  further  than  they  are  given  in  the  preced- 
ing three  Tables  and  the  Notes  accompanying  them. 


* But  in  the  second  part  of  this  Class  we  have  the  Useful  Arts.  They 
take  the  results  of  the  General  Facts  obtained  by  the  Sciences  in  the  First 
Department  of  the  first  Class,  and  the  Laws  obtained  in  the  corresponding 
Department  of  the  second  Class,  and  hy  Deduction  apply  them  to  the  results 
which  minister  to  man’s  physical  and  temporal  wants,  as  being  subservient 
to  the  purposes  of  life  ; which  purpose  again  is  the  attainment  of  that  End 
or  Destiny  for  which  his  Creator  placed  him  in  this  state  of  existence. 


TV.]  METHODS  OF  INSTRUCTION  AND  CRITICISM. SECT.  H.  347 


SECTION  H. 

Of  the  Conveyance  of  Ideas  from  one  Mind  to  another. 

1247.  All  Methods  in  so  far  as  they  belong  to  the 
Sphere  of  Logic,  are  determined  by  the  Idea  of  the 
True.  They  aim  merely  to  satisfy  the  demands  of 
comprehension  and  conviction.  Blit  most,  if  not  all, 
the  Methods  of  Argument  and  Instruction  Method.  of 
come  also  within  the  Sphere  of  Rhetoric,  lo gfc  and  of 
They  aim  not  only  to  convince,  hut  also  to  ' e °nc' 
please  and  to  persuade  ; and  in  Instruction  especially, 
to  save  time  and  labor,  and  to  facilitate  the  ease  with 
which  we  remember  what  we  have  once  learned.  But 
the  Methods  of  Rhetoric  are  determined  by  the  Idea 
of  the  Useful.  Its  precepts  are  valuable  only  because 
they  are  useful — useful  for  pleasing  and  persuading — 
useful  for  the  perspicuity  of  statement — lucidness  of 
illustration  or  impressing  upon  the  mind  a sense  of  the 
importance  of  what  is  communicated. 

1248.  It  is  obvious,  therefore,  that  by  far  the  largest, 
though  by  no  means  the  most  important,  Methods  of 
part  of  what  properly  belongs  to  any  ade-  struction. 
quate  discussion  of  the  Methods  of  Instruction,  must 
come  within  the  appropriate  sphere  of  Rhetoric.  I 
shall,  therefore,  make  but  a very  short  Chapter  on  the 
Method  of  Instruction  in  this  place. 

1249.  By  Instruction  we  mean  not  merely  the 
communication  of  the  knowledge  which  we  instruction  and 
have  obtained.  Our  attention  is  much  more  construction, 
completely  fixed  upon  the  means  of  Construction , or 
the  putting  it  into  a system,  and  so  arranging  the  parts 

. as  that  they  may  best  fulfil  the  conditions  of  a thorough 
comprehension  of  the  general  subject  by  those  who  are 
unacquainted  with  it. 

1250.  I regard  it  as  a controlling  fact  in  regard  to 
Methods  of  Instruction,  that  a conception  conceptions 
cannot  be  conveyed  or  transferred,  as  a m™i°AbedC0I£ 
whole,  from  one  mind  to  another.  Each  one  Wholes- 


348 


LOGIC. — PAKT  n. 


[chap. 


must  be  formed  de  novo  in  each  mind.  No  one  can 
convey  bis  sensation  to  another  ; we  can  describe  them 
to  those  beings,  and  those  only  who  have  had  sensa- 
tions of  the  same  species — the  sensation  of  color,  for 
instance,  which  I have  when  I look  at  the  object  before 
me,  I cannot  communicate  to  any  other  person.  If 
he  can  see,  I can  describe  it  to  him  so  that  lie  can  form 
a conception  of  it.  But  if  he  be  blind,  he  cannot  con- 
ceive of  a sensation  of  color,  nor  can  one  be  conveyed 
into  his  mind. 

1251.  A judgment  may  be  conveyed  from  one  mind 
judgments  to  another,  provided  both  minds  have  the 

may-  conceptions  which  constitute  the  matter  of 

the  judgment.  Thus  if  I affirm  that  “ gold  is  yellow,” 
the  person  hearing  me  does  not  need  to  judge  whether 
it  is  yellow  or  not,  in  order  to  understand  my  judg- 
ment, or  the  proposition  affirming  it — the  proposition 
conveys  the  judgment  to  his  mind,  and  he  may  then 
affirm  or  deny  it  as  he  pleases. 

1252.  But  a conception  cannot  be  conveyed  in  that 
way  or  in  any  way.  It  is  necessarily  constructed  by 

and  within  every  mind  in  which  it  can  exist 
may  be  mean"!  at  all.  Thus  suppose  I have  a conception  of 
known s'lor  an  an  object,  and  use  some  word  in  an  unknown 

unknown  word.  . ° . . . . i . 

tongue  to  express  it,  that  word  is  just  as  good 
in  itself  as  any  other,  and  j ust  as  good  relatively  to  all 
who  understand  the  language  to  which  it  belongs. 
But  it  has  no  power  of  itself  to  convey  or  suggest  the 
conception.  If  the  conception  is  one  which  has  been 
already  formed,  and  is  in  the  mind  of  the  person  to 
whom  I am  speaking,  all  that  I need  to  do  is  to 
define  my  word  by  giving  its  synonyme  in  the  lan- 
guage which  he  uses.  If  I had  used  the  word  “ calebfi 
which  is  Hebrew,  I have  but  to  give  the  English 
word  “ dogfi  and  I have  defined  the  word  and  re- 
called to  his  attention  the  conception  which  the  two 
words  are  used  to  represent  in  their  respective  voca- 
bularies. 

1253.  But  suppose  the  conception  be  entirely  new 


IV.]  METHODS  OF  INSTRUCTION  AND  CRITICISM. SECT.  IH.  349 

to  tlie  person  addressed,  no  mere  definition  of  the  word 
by  which  I denote  it  will  suffice.  I must  verbal  Defini- 
give  him  first  the  Essentia  of  the  object  by  c°n4yweoncep- 
referring  it  to  the  Proximate  Genus,  and  tlons- 
then  the  Differentia,  which  distinguishes  it  from  the 
coordinate  species  in  that  Genus.  And  then  further 
if  it  be  an  individual  object,  I must  give  some  of  the 
individual  marks  or  inseparable  accidents. 

1254.  The  person  addressed  then  takes  up  together 
(for  that  is  the  meaning  of  the  word  11  conceive'’),  all 
the  matter  which  I have  given  and  puts  it  The  person  ad- 
together  in  his  own  mind,  as  I gave  it  to  ^„e&dtheeconf 
him,  and  he  has  the  conception  which  I ception- 
had.  But  he  has  formed  it  anew  in  his  own  mind  ; I 
gave  him  the  material  only.  I defined  my  conception 
by  an  analysis  of  its  matter,  and  he  constructed  his  by 
a synthesis  of  the  same  matter. 

1255.  But  each  of  these  elements  into  which  I 
resolved  my  conception  by  analysis,  and  out  of  which 
he  constructed  his  by  synthesis,  are  also  conceptions 
conceptions  ; and  if  they  are  conceptions  ^ui0zned  m,nto 
which  he  has  not  already  formed,  he  is  not  |^e  ec’0e”®£: 
prepared  to  synthesize  out  of  the  material  tions- 
which  I have  given  him.  My  Definition  has  not  been 
sufficiently  elementary,  I must  go  back  one  step  further 
and  define  the  elements  of  which  he  has  not  yet  formed 
a conception. 


SECTION  HI. 

Of  Definition  and  Description. 

1256.  The  predicating  of  any  subject  its  Essentia 
and  Differentia  is  what  is  called  Definition.  Definition. 
Thus  if  I say,  “ Mahomet  was  the  man  who  founded 
the  religion  called  by  his  name,”  I give  first  the  Essen- 
tia— what  he  was — “ a man  ; ” and  secondly,  Where 
the  Differentia,  which  distinguishes  him  from  qua“- 
all  other  men  “ who  founded  the  religion ,”  &c.  By 
these  words  I have  given  an  adequate  definition. 


350 


LOGIC. — PART  II. 


[CHAP. 


1257.  But  suppose  I had  omitted  the  Essentia,  and 

specific  Defi-  said,  “ he  was  the  founder  of  the  religion, ” 
quate.  &c.?  this  would  be  a specific  definition  ; but 

the  question  might  still  recur  as  to  his  Essentia,  whe- 
ther he  was  “ man,”  “ angel,”  or  “ demon.”  In  that 
case  the  definition  would  have  been  inadequate,  inas- 
much as  “ founder  of  the  religion,”  &c.,  may  be  the 
Differentia  of  Species  in  several  different  Proximate 
Genera,  as  “ man,”  “ angel,”  &c. 

1258.  Or  again,  suppose  I had  merely  said,  “ Ma- 
homet was  a man  of  Arabia .”  Here  the  Essentia 
Definitions  of  in-  “man”  would  be  satisfactory  to  give  me  a 
eiv^thebnTvf  distinct  conception,  but  the  words  “ of  Ara- 
Snai  marks.  tfia,”  are  no  Differentia  of  an  individual 
man,  since  there  are  many  “ men  of  Arabia.”  The  De- 
finition would  be  inadequate.  It  would  not  be  definite. 
It  would  give  the  Essentia  with  the  Differentia  of  the 
species,  but  no  peculiar  or  distinguishing  mark  of  the 
individual. 

1259.  A Definition  is  either  of  a name  or  of  the 
Definition  ofa  conception  which  we  have  of  a thing,  or  of 

ception°  orc°of  the  thing  itself  by  means  of  its  conception 
or  name. 

1260.  When  we  define  a name  or  a word,  we  ex- 

Definition  of  a plain  its  meaning  by  other  words  having 
name.  the  same  meaning.  Thus  we  define  cjnXeco 

in  Greek  and  arno  in  Latin,  by  the  word  “ love  ” in 
English.  We  explain  the  name  “ sulphuric  acid,”  by 

verbal  Defini-  saying  that  it  is  the  “ oil  of  vitriol.”  This 
tions.  is  called  a Verbal  Definition,  as  merely  de- 

fining words. 

1261.  A real  Definition  is  one  that  defines  the  thing 
itself  of  which  the  conception  is  formed.  But  as  we 

Real  Defini-  know  the  thing  or  subj  ect-matter  only  by  the 
lions.  conception  which  we  form  of  it,  we  can  of 

course  define  it  only  by  means  of  that  conception.  To 
define  any  thing,  therefore,  is  to  define  or  give  by 
analysis  the  conception  which  we  have  of  it.  Our  con- 
ception may  be  compared  by  this  means  with  those 


IV.]  METHODS  OF  INSTRUCTION  AND  CRITICISM. SECT.  III.  351 

which  other  persons  have  of  the  same  object,  and  cor- 
rected, if  found  to  be  erroneous  or  inadequate,  by  means 
of  theirs.  This  correction,  however,  implies  that  their 
means  and  opportunities  of  investigation  have  been 
superior  to  ours. 

1262.  We  may,  however,  sometimes  enable  another 
to  form  a concejition  of  the  thing  itself,  with-  Descriptions 
out  the  intervention  of  any  conception  which  conve?in“conf 
we  may  have  formed  of  it  ourselves.  This  ceptions- 

we  do  by  a Description  pointing  to  the  place  in  which 
it  is  situated,  the  time  when  it  occurs,  or  the  circum- 
stances by  which  it  is  surrounded.  ^In  this  case  we 
simply  refer  to  the  sphere  of  its  conception,  and  leave 
others  to  learn  the  matter  for  themselves  by  their  own 
observations  or  investigation. 

1263.  It  has  been  very  generally  held  that  there 
are  certain  simple  Ideas  and  ultimate  elements  in  all 
conceptions  which  cannot  be  defined.  And  the  reason 
given  for  the  opinion  is,  that  being  simple  or  ultimate 
elements  they  can  be  divided  or  analyzed  no  farther. 

1261.  But  this  is  evidently  a mistake.  We  do  not 
analyze  the  object  in  our  definition,  but  only 
our  conception  of  it.  JNow  a conception  ex  tion  that  can- 

• , • • ° • . r*  not  be  defined. 

m termini  can  never  consist  ot  a simple  ele- 
ment.  It  is  the  taking  together  of  several  properties  as 
Essentia  and  Differentia  into  a Logical  Whole  which 
to  the  mind  represents  the  object  denoted  by  the  term 
which  represents  the  conception.  We  get  a conception 
of  an  object  only  by  its  Essentia  and  Differentia.  And 
here  the  conception,  including  these  elments,  can  be 
analyzed  and  so  defined.* 

* We  must  remember  that  it  will  often  happen  that  the  Differentia  of 
any  object,  or  class  of  objects,  as  we  form  our  conceptions  of  them,  will  not 
consist  of  properties  which  can  be  predicated  of  the  objects  considered  solely 
and  by  themselves.  They  are  rather  relative  properties.  Thus  we  may  predi- 
cate “ hardness”  of  iron  in  and  by  itself ; but  “ magnetism”  is  but  a relative 
property,  since  we  could  never  know  its  reality  except  by  the  relation  which 
the  magnetic  body  sustains  to  others  which  are  attracted  by  it  while  in  that 
condition.  So  with  “ causality,”  and  many  of  the  other  elements  which 
enter  into  our  conceptions ; they  indicate  rather  the  relations  which  the 
objects  sustain  to  others,  than  any  properties  which  are  directly  perceptible 
by  themselves. 


352 


LOGIC. PAKT  n. 


[CHAP. 


1265.  The  difficulty  however  is  in  us.  It  is  often 
the  case  that  we  have  a distinct  conception  without  its 

Reasons  why  being  definite  in  our  own  minds.  We  never 
timesarunabTteo  have  analyzed  it,  and  perhaps  cannot  analyze 
define.  it  g0  as  to  name  each  element  of  its  matter, 
and  say  what  precisely  is  its  Essentia  and  what  its 
Differentia.  Thus  I suppose  all  persons  have  a pretty 
distinct  conception  of  an  apple.  But  I doubt  if  any 
one  can  give  the  Differentia  of  it  so  as  precisely  to 
draw  the  line  between  it  and  the  pear  for  instance. 

1266.  Again  there  are  objects  the  definition  of 
which  is  made  difficult,  and  practically  impossible  in 

want  of  gene-  some  cases,  by  our  having  no  well  known 
rai  terms.  Proximate  Genus  to  which  to  refer  them  as 
expressive  of  their  Essentia.  Thus  Prof.  Loomis,  in  his 
Geometry,  in  attempting  to  define  a “ straight  line,” 
says,  “ It  is  the  shortest  path  between  two  points.”  The 
Differentia,  “ shortest  between  two  points,”  is  fault- 
less. But  the  Essentia,  “ path,”  sounds  strangely.  A 
line  is  not  a “path”  in  any  sense  in  ivliich  we  are 
accustomed  to  that  word  ; that  is,  a “geometrical  line” 
does  not  belong  to  any  genus  which  we  are  accustomed 
to  denote  by  the  word  “ path.” 

1267.  This  is  in  fact  a difficulty  often  met  with. 
We  may  have  the  Differentia  of  a conception  at  our 
a frequent  dif-  command,  but  not  its  Essentia.  In  all  at- 
ficu|ty-  tempts  to  define  “ consciousness ,”  for  exam- 
ple, the  same  difficulty  is  encountered.  Shall  we  call 
it  a “ faculty,”  a “ function,”  or  simply  a “ state  ” of 
the  mind  ? 

1268.  The  usual  resort  in  such  cases  of  our  inability 
to  define  that  of  which,  however,  we  have  a definite 

The  usual  re-  but  no  distinct*  conception,  is  to  describe' 
80rt-  the  sphere  by  means  of  the  Differentia,  and 

leave  the  Genus  or  Essentia  undetermined. 

1269.  But  an  adequate  Definition  defines  its  object 
by  referring  it  to  its  species  and  genus.  Thus  we  say 

* It  may  be  well  to  remark  that  the  Essentia  makes  a conception 
“ distinct"  the  Differentia  makes  it  “ definite." 


IV.]  METHODS  OF  INSTRUCTION  AND  CRITICISM. — SECT.  m.  353 

that  “ Iron  is  a metal  of  great  malleability , density , 
and  of  a darkish  gray  color.”  When  we  say  What  consti. 
it  is  a “ metal,”  we  refer  it  to  the  genus  ‘“‘aetse  anDe^: 
“ metals  ; ” and  of  course  we  may  thereafter  tion- 
predicate  of  it  all  the  Essentia  of  metals.  By  saying 
“ it  is  of  great  malleability,  density,  and  of  a darkish 
gray  color,”  we  refer  it  to  each  of  the  species  whose 
Differentia  are  respectively  “ malleability,”  “ density,” 
and  “ gi’ay  color.” 

1270.  We  are  said  to  define  a conception  generally 
or  qenerically.  when  we  refer  it  to  its  nenus, 

u,,  • ° • 755  • /?  77  ^ 7 Generic  Defi- 

as  “ man  is  an  animal  / specifically,  .when  nitions  sped- 
we  give  the  Differentia  of  the  species  with- 
out the  genus,  as  “ man  is  rational ,”  or  “ a being  with 
reason  ; ” accidentally , when  we  give  merely  Accidental, 

some  accidental  property  of  the  object ; phy-  physical. 
sically , when  we  enumerate  the  physical  parts,  as 
“ man  has  two  hands,  two  feet,  erect  form ; ” and 
metaphysically , when  we  refer  to  the  invi-  Metaphysical, 
sible  nature,  as  “ man  is  a spiritual  being,  with  reason, 
intellect,  memory,  conscience,”  &c.* 

1271.  In  defining  a Genus,  as  such,  the  Essentia 
only  can  be  given. f But  in  defining  a Species,  both 
the  Essentia  and  the  Differentia  must  be 

• i • ixi*  Ti**iiii  AVho.t  Defini- 

given  ; and  m denning  an  Individual  there  tions  can  be 
must  be  added  to  the  Essentia  and  Differ-  gnen' 
entia  the  peculiarities  which  distinguish  the  Individual 
defined  from  others  of  the  same  species. 

1272.  But  when  a Definition  fails  to  fulfil  these 
conditions,  as  if  in  defining  a Species,  there  inadequate  De- 
is an  omission  of  the  Differentia ; or  in  detin-  finitioift- 
ing  an  Individual  an  omission  of  the  peculiarities,  the 
definition  is  inadequate. 

* What  is  sometimes  called  a Negative  Definition,  or  defining  negatively, 
is  no  definition  of  the  subject  at  all.  It  consists  merely  in  naming  the  Dif- 
ferentia of  the  coordinate  species,  and  saying  that  they  are  not  properties 
of,  and  do  not  belong  to  the  Species  which  we  are  defining. 

f We  may  of  course  refer  it  to  the  next  higher  of  the  subaltern  Genera, 
in  which  case  it  becomes  a Species  to  be  defined  as  such  by  the  Essentia  of 
its  Proximate  Genus  and  its  own  Differentia. 


354 


LOGIC. — PART  n. 


[chap. 


1273.  Definition,  therefore,  always  implies  a classi- 
Definiiion  im-  fication  of  the  thing1  defined,  by  referring  it 

tion.  ' to  its  Genus  and  Species.  Hence  it  appears 
that  we  can  cognize  the  Individual  only  through  the 
Species.  Each  property  which  we  ascribe  to  it  or  see 
that  it  possesses  refers  it  to  a class,  whose  Differentia 
is  the  property  thus  ascribed  to  the  individual  object. 

1274.  One  of  the  readiest  and  best  illustrations  of 
this  principle  is  afforded  in  the  conjugation  of  the  verb. 

The  conjuga-  The  verb  itself  is  the  Genus,  and  its  Essentia 
sion  ofyerbaTii  the  meaning  of  the  word  in  its  most  general 
illustration.  sense.  The  Species  is  the  voice,  as  active, 
passive,  &c.,  whose  Differentia  is  the  mode  of  the 
action  of  the  verb  in  reference  to  the  agent  and  the 
object.  Mood  is  the  first  sub-species,  the  Differentia 
of  which  is  the  mode  of  affirmation  as  declaring  (In- 
dicative), representing  it  as  possible,  &c.  The  second 
sub-species  is  Tense,  and  its  Differentia  is  the  relation 
of  the  action  to  the  time  in  which  the  word  is  used  by 
the  speaker.  The  next  sub-species  is  “ number,”  indi- 
cating as  its  Differentia  whether  the  subject  of  the  verb 
included  one  or  more  ; and  the  infima  species  is  the 
“ person,”  limiting  by  its  Differentia  the  subject  still 
further,  by  showing  whether  the  subject  is  the  person 
speaking,  the  person  spoken  to,  or  some  person  spoken 
of.  And  the  word  itself,  as  it  stands  on  the  written 
page,  or  is  heard  in  oral  speech,  is  the  individual. 

1275.  It  is  very  likely  to  happen  that  the  terms  used 
in  any  Definition  will  also  need  to  be  defined.  In  this 

case  the  laws  of  Definition  are  the  same  as 
to  define1 before ; we  define  by  Essentia  and  Differentia 
still.  Thus  if  I should  define  the  palm  as 
“ an  endogenous  tree,”  &c.,  one  might  be  wholly  un- 
able to  construct  the  conception,  because  he  had  not 
previously  the  conception  for  which  “ endogenous  ” 
stands.  I should  then  be  obliged  to  define  that  con- 
ception by  giving  its  conception,  as  applied  to  plants — 
growth  Inj  mccesive  additions  to  the  inside.  But  sup- 
pose my  definition  were  not  yet  sufficiently  elementary, 


IY.]  METHODS  OF  INSTRUCTION  AND  CRITICISM. SECT.  HI.  355 

and  that  he  had  no  definite  conception  of  “ growth,” 
I should  he  obliged  to  define  it  as  a species  of  the 
genus  “ increase,”  giving  the  Differentia  which  distin- 
guish it  from  the  coordinate  species — accretion , agglo- 
meration, &c.  Or  suppose  the  words  “ by  successive 
additions  to  the  inside,”  represented  a conception  not 
previously  formed  in  the  mind  of  the  person  addressed, 
I should  have  to  explain  or  define  them  in  the  same 
way,  either  showing  what  an  “ addition  ” is,  or  the 
difference  between  the  kind  that  is  “ to  the  inside,” 
and  that  which  is  “ to  the  outside,”  its  coordinate. 

1276.  Hence  as  each  Definition  may  need  a defini- 
tion of  its  terms,  there  must  be  a constant  ultimate 
retrogression  until  we  come  to  some  ultimate  conceptions, 
conception,  which  is  formed  at  the  first  sight  of  the  ob- 
ject ; or  to  Description,  pointing  out  the  sphere  of  the 
object  of  which  the  conception  is  to  be  found. 

1277.  A Description,  therefore,  does  not  furnish  the 
material  for  the  construction  of  a conception.  A Description 
It  merely  informs  us  when,  or  where,  or  how  MeM^uerShibr 
we  may  find  it  for  ourselves.  And  the  pro-  a conception, 
cess  of  finding  it  is  one  of  the  original  Methods  of  In- 
vestigation. It  brings  us  back,  therefore,  to  primary 
or  elementary  conceptions. 

1278.  These  primary  or  elemental  conceptions  of 
external  objects  are  formed  spontaneously,  Primary  Con. 
and  of  necessity  are  the  perception  of  the  tlneiuTandSe- 
external  senses.  And  of  invisible  objects,  cessary- 
such  as  geometrical  figures,  &c.,  they  are  formed  by 
the  Reason  constructing  them  in  the  mind  itself.  Thus 
suppose  I imagine  a point  moving  from  one  position  in 
space  always  at  the  same  distance  from  another  point, 
until  it  comes  back  to  the  place  of  its  departure,  I have 
formed  the  conception  of  a circle  by  constructing  the 
circle  itself.  It  is  for  Genus  a figure  in  space,  and  for 
Differentia  it  has  a circumference  every  point  of  which  is 
equally  distant  from  one  and  the  same  point  within  it. 

1279.  But  this  Genus,  “ figures  in  space,”  cannot 
be  a nrimary  conception  for  us,  since  we  never  have 


356 


LOGIC. — PART  n. 


[CHAP. 


the  Differentia  denoted  by  the  words  “ in  space,”  ex- 
conceptions of  cept  as  a counterpart  to  objects  having  shape 
trathteSJip5y  °a  and  outline  in  the  external  world  or  in  place. 
S'™  of  relf-  I do  not  deny  that  the  conception  would  be 
ities  of  being,  possible  without  such  observation.  That  is 
a question  of  metaphysics  with  which  we  have  nothing 
to  do  in  this  place.  But  as  a fact,  all  mortals  here  on 
Earth,  do  not  form  conceptions  of  the  invisible  realities 
of  truth,  until  after  experience  of  the  visible  realities 
of  being  in  the  material  world. 


SECTION  IY. 

Of  Natural  and  Artificial  Classifications. 

1280.  The  conception  of  each  individual  object — for 
with  the  individual  we  always  begin  in  actual  expe- 
rience— is  formed  by  means  of  the  Essentia 

first" form e d‘u ff-  and  Differentia.  I see  an  object  before  me 
those  mode  by  winch  is  yellow  and  round ; it  1 call  it  an 
“ orange,”  I refer  it  to  a conception  already 
formed,  and  consequently  this  is  not  a primary  one.  It 
is,  however,  the  point  at  which  each  of  us  who  live  at 
the  present  day  begin  with  the  formation  of  our  con- 
ceptions. We  learn  the  names  that  have  already  been 
given  to  things,  and  base  our  classifications  and  con- 
ceptions upon  those  that  have  been  made  before  us. 

1281.  The  primary  classifications  are  always  of 
necessity  very  simple  and  unscientific.  They  are  based 

on  some  property  immediately  obvious  to 
ficadons  very  the  senses,  as  color,  shape,  odor,  &c.,  lor 
their  Essentia.  The  next  step  is  a division  of 
the  Genera,  using  different  colors,  odors,  shapes,  &c., 
as  Differentia.  This  classification  is  almost  instanta- 
neous if  not  quite  so,  at  the  first  instant  when  the  mind 
is  awakened  to  activity  by  the  presence  of  material 
objects  to  our  senses. 

1282.  From  these  first  and  purely  accidental  prin- 
cioles  of  classification,  we  pass  on  in  our  progress  of 


IV.]  METHODS  OF  INSTRUCTION  ANT)  CRITICISM.— SECT.  IV.  357 

comprehension,  at  each  step  adopting  as  permanent 
and  useful  such  as  have  been  found  so  in  Someofthem 
times  past,  and  because  they  have  been  so  bca”f in  Qf  iLhne 
found  have  received  those  common  names  suase- 
which  constitute  the  basis  of  all  languages,  as  “ com- 
mon names.” 

1283.  But  no  sooner  do  we  begin  our  scientific 
investigations  than  we  find  in  most  cases 
that  a new  classification  becomes  requisite,  new  ciassifica- 
one  requiring  for  its  construction  a new  lons' 
analysis  of  the  objects  to  be  included  in  the  classes. 

1281.  Hence  the  distinction  between*  natural  and 
artificial,  or  scientific  classifications.  ISTatu-  Distinction  be- 
ral  classifications  are  such  as  are  formed  at  indensdeS 
once  instinctively  and  of  necessity  by  the  Clas5lficat10"3' 
mind.  They  are  based  upon  the  more  obvious  and 
conspicuous  properties  of  the  objects,  and  denoted 
by  such  words  as  the  common  names  of  all  languages. 
The  scientific  classifications,  on  the  other  hand,  are 
such  as  are  based  upon  less  obvious  properties,  and  are 
devised  for  the  purpose  of  expediting  Science.  They 
are,  for  the  most  part,  denoted  by  what  are  called  the 
technical  terms  of  a language  or  science. 

1285.  The  problem  in  all  scientific  classifications  is 
to  group  together  in  one  species  those  facts  which  have 
the  greatest  number  of  properties  in  com- 

mon,  and  to  classify  on  those  properties  in  scientific 

i • i i i ^ i <•  Classifications. 

which  are  regarded  as  h ormal  with  reference 
to  those  which  are  Modal.  The  fewer  the  classes 
therefore  the  better,  provided  that  in  reducing  the 
number  of  classes  we  do  not  increase  the  exceptions  to 
each,  so  as  to  make  the  aggregate  of  Species  and  Ex- 
ceptions greater  than  in  some  other  classifications. 

1286.  Thus  to  take  an  example  from  Ethnology. 
If  we  divide  men  into  three  coordinate  classes,  red, 
black,  and  white,  not  only  are  the  Modal  An  illustration 
properties  common  to  each  species  in  classi-  from  Ethnology, 
fication  few,  but  the  exceptions  to  any  statement  that 
might  be  made  concerning  any  one  of  the  speeies  are 


358  LOGIC. PART  II.  [CHAP. 

very  numerous.  As  the  result  of  much  investigation, 
it  has  been  found  that  if  we  class  them  as  woolly- 
headed,  bearded,  and  beardless,  the  number  of  state- 
ments, including  both  the  rules  and  the  exceptions, 
requisite  for  a full  treatise  on  the  Natural  History  of 
Man,  is  greatly  reduced.  Of  course,  therefore,  that 
natural  history  when  thus  presented,  is  much  more 
easily  and  much  more  quickly  learned,  and  longer 
remembered  than  when  presented'  to  the  mind  of  the 
learner  by  means  of  any  other  classification. 

1287.  To  take  another  illustration.  In  Botany  the 
primary  classification  of  its  objects  was  into  Trees, 

illustration  Shrubs,  and  Plants.  CLesalpinus  proposed 
fromuP history  the  first  scientific  classification  based  on  “ the 
number,  position,  and  figure  of  organs,”  as 
“ the  flower,  the  seed  receptacle,  and  the  seeds  ; ” for 
the  purpose,  as  he  said,  of  “ ranging  them  into  bri- 
grades,  regiments,  and  companies,  like  a well-ordered 
army.”  Soon  after  Bauiiin  undertook  another  and 
simpler  classification.  Ray  proposed  another ; and 
in  1687  Tournefort  proposed  to  classify  on  “ the  regu- 
larity or  irregularity  of  the  flowers  in  form,  and  by 
the  situation  of  the  receptacle  of  the  seeds  below 
the  calyx  or  within  it.”  Then  Linnaeus  appeared  and 
classified  by  “ the  pistils  and  stamens  of  the  flowers.” 
And  finally,  we  have  the  system  of  the  Jussieus,  based 
on  “ the  number  of  the  cotyledons  and  the  structure 
of  the  seeds,  and  subordinate  to  this  the  insertion  of  the 
stamina,  as  over,  about,  or  under  the  germen.” 

1288.  A primary  object  is  undoubtedly  to  make  the 
number  of  the  species  as  small  as  practicable.  And 

■me  limit  to  the  limit  to  this  reduction,  as  has  been  said, 
ofetherenumber  ‘s  the  number  of  exceptions  and  abnormal 
species.  peculiarities  which  always  increases  with  the 
reduction  in  the  number  of  classes,  so  long  as  we  ad- 
here to  the  same  principle  of  classification.  And  that 
principle  which  will  give  us  the  smallest  aggregate  of 
species  and  of  exceptions,  is  said  to  be  the  simplest  or 
to  simplify  the  classification  the  most. 


IV.]  METHODS  OF  INSTRUCTION  AND  CRITICISM. SECT.  IV.  359 


1289.  Now  wherever  we  begin  in  our  instruction, 
whether  with  the  most  general  subject,  as  in  the  Syn- 
thetic Method — or  with  the  individual,  as  in  We  must  de. 
the  Analytic,  we  must  define  our  subject,  tX 
and  each  subject  as  we  pass  along,  by  refer-  sdSfic  etas'! 
ring  it  to  the  natural  and  well-known  classi-  61fications' 
fications.  And  if  we  have  adopted  a scientific  classifi- 
cation, we  need  always  to  give  the  common  one  also, 
and  explain  ours  by  the  difference  between  them. 
Thus  a chemist  would  say,  “ chloride  of  sodium  is 
the  muriate  of  soda  of  the  old  classifications  — the 
common  salt  of  the  common  use.  It  consists  of  so 
many  parts  of  sodium,  so  many  of  chlorine,”  &c.,  &c. 

1290.  In  the  course  of  our  classifications  we  shall 
sometimes  encounter  a phenomenon  which  similar  Differ- 
we  have  not  yet  noticed — namely,  the  recur-  ®ntia proximate 
rence  of  the  same  Differentia  of  Species  in  G6nera- 
different  Proximate  Genera — these  we  may  cfesCurring  Spe_ 
call  Recurring  Species. 

1291.  Thus  in  Mathematics  we  have  “ curved  lines  ” 
and  “ curved  surfaces,”  in  which  the  Genera  “ lines  ” 
and  “ surfaces  ” comprehend  Species,  whose  illustrated 
Differentia  is  “curved;”  as  “curved  lines,”  [™3mSndthfrom 
and  “ curved  surfaces.”  Again  in  Gram-  Grammar- 
mar,  in  the  conjugation  and  declension  of  the  Verb, 
we  have  three  voices,  for  instance,  Active,  Passive, 
and  Middle.  Now  taking  these  as  Proximate  Genera, 
we  have  in  each  of  them  the  same  Differentia  of 
Mood,  Infinitive  Mood,  &c. ; and  the  Differentia,  that 
is,  the  signification  and  force  of  Mood  is  precisely  the 

_ same  in  one  voice  as  in  the  other,  although  modify- 
ing a different  Essentia.  -So,  also,  each  Mood  has  dif- 
ferent Tenses,  as  a Present,  and  Past,  and  a Future. 
The  force  or  Differentia  of  Tense  is  precisely  the  same 
in  one  Mood  as  in  the  other.  It  is  defined  as  deter- 
mining “ the  time  at  which  the  Verb  represents  the  act 
as  taking  place  ; ” the  Present  represents  it  as  taking 
place  at  the  time  of  speaking,  whether  in  one  Mood 
or  mode  of  representing  the  action  or  another,  and  irre- 
spective of  the  Differentia  of  voice. 


360 


LOGIC. — PAItT  II. 


[CHAP. 


SECTION  V. 

Of  the  Division  of  the  General  Subject. 

1292.  The  subjects  of  which,  we  treat  have  exten- 
sion in  two  different  directions,  Comprehension  and 

two  kinds  of  Protension.  If  we  are  treating  a general 
sion™ma*Gene-  subject,  as  Chemistry,  Mechanics,  &c.,  it  has 
mi  subject.  Comprehensive  Extension,  and  admits  of 
course  of  division  into  subordinate  parts.  If  we  are 
treating  of  an  individual  subject,  as  the  history  of  a 
nation,  the  biography  of  an  individual,  it  has  Proten- 
sive  Extension  only. 

1293.  In  this  latter  case  there  is  no  logical  neces- 
sity for  a division  at  all.  A division  is  only  a conve- 

Noioicaine  nience>and  one  that  is  often  of  very  great 
visfony°  oF1 pm'  imP01'tailce  both  to  the  writer  and  the  reader, 
tensive  Exten-  And  as  it  is  one  that  is  required  and  deter- 
mined rather  by  the  idea  of  Utility  than  the 
idea  of  Truth,  we  will  leave  its  discussion  to  the  Rhe- 
toricians. 

1291.  But  in  treating  of  a general  subject  a division 
becomes  necessary,  in  consequence  of  the  fact  that 

d.  . jon  f a much  which  it  is  necessary  to  say,  may  be 
Generalsubject  predicated  of  a part  of  the  included  indi- 
vidual subjects  which  cannot  be  predicated 
of  the  wdidle  ; and  much  of  some  parts  which  cannot  be 
predicated  of  others. 

1295.  If  the  subject  will  admit  of  a division  into 
coordinate  parts,  it  is  best  to  divide  in  that  way.  And 

coordinate  then  the  division  is  to  be  determined  by  the 
pan  preferable.  }aw  already  laid  down  for  scientific  classifi- 
cations ; namely,  so  divide  as  that  the  aggregate  of  the 
number  of  the  parts  and  of  the  exceptions  to  the  predi- 
cates affirmed  of  the  parts,  will  be  the  smallest  that  the 
nature  of  the  matter  will  allow. 

1296.  The  reason  for  this  rule  is  the  same  as  that 
given  above.  The  instruction  can  be  given  in  fewer 


TV.]  METHODS  OF  INSTRUCTION  AND  CRITICISM. — SECT.  VI.  361 

words,  consequently  in  shorter  time,  is  more  easily  and 
sooner  understood  and  better  remembered,  Reasonforthe 
than  when  the  mind  is  encumbered  by  a Rute- 
multiplicity  either  of  subdivisions  or  of  exceptions  to 
the  statements  made  for  general.  Each  coordinate  and 
each  subordinate  part,  as  well  as  each  exceptional  case 
or  individual,  becomes  a separate  and  distinct  subject  of 
predication,  which  it  takes  as  long  to  teach  and  requires 
as  much,  and  often  more,  effort  to  remember  than  the 
most  comprehensive  statement  in  the  whole  science. 

1297.  But  there  are  cases  in  which  no  division  into 
coordinate  parts  can  he  made  unless  it  be  a very  clumsy 
one.  Our  present  general  subject  (828),  “ Me-  Il?  some  casca 
thod,”  as  has  been  already  said  is  such  an  |p|ate“?ait3 
one.  Again,  if  one  were  treating  of  the  imp°ssibIe- 
Literary  Men  of  a nation,  it  would  be  impossible  to 
make  a coordinate  division  that  would  answer  any 
good  purpose. 

1298.  In  such  cases  we  must  divide  into  Alternate 
Species.  As  in  the  case  just  named,  we  might  divide 
the  Literary  Men  into  Historians,  Poets, 

Essayists,  Philosophers,  Naturalists,  Ac.  Alternate1  s"e 
This  would  be  a useful  division.  But  the 

same  man  might  be  distinguished  in  more  than  one  of 
the  classes  named,  as  for  instance,  the  English  Southey 
as  a poet  and  as  a historian ; Coleridge,  a poet  and  a phi- 
losojiher  ; Macaulay  as  a poet,  historian,  and  essayist. 

1299.  And  with  regard  to  the  number  of  Alternate 
Parts  into  which  the  General  Subject  should  The  same  rule 
be  divided,  the  same  rule  holds  as  above  : number  of  Al- 
it  should  be  the  minimum  aggregate  of  parts  cdorAatespL 
and  exceptions. 


SECTION  VI. 

Of  the  Order  in  the  treatment. 

1300.  In  the  first  acquisition  of  knowledge  we  are 
obliged  to  begin  with  the  individual  and  concrete,  and, 

16 


362 


LOGIC. — PART  II. 


[chap. 


examining  them  one  by  one,  we  ascend  to  the  general  and 
the  abstract.  Thus  the  knowledge  of  human 
know^vith  the  nature  is  acquired  by  an  acquaintance  with 
individual  men  one  after  another,  analyzing, 
abstracting,  and  omitting  what  is  peculiar  to  each,  and 
retaining  as  the  matter  of  the  conception  to  be  ex- 
pressed by  one  general  term  “ man,”  all  that  is  com- 
mon to  all  men. 

1301.  So,  too,  in  acquiring  the  knowledge  of  any 
we  also  learn  particular  or  individual  object,  we  may  per- 
by  one.  ceive  its  properties,  many  ot  them  at  a tune. 
But  we  have  to  learn  or  study  them,  property  after 
property,  one  at  a time. 

1302.  Now  in  teaching  others,  which  is  instruction, 
we  may  pursue  the  same  method  ; beginning  with  the 

■rhe  Analytic  individual  and  the  concrete,  and  proceed  to 
Method  in  the  general  and  abstract.  This  is  called  the 
Analytic  Method  of  teaching.  But  it  is  gene- 
rally found  tedious,  uninteresting,  and  unsatisfactory. 
And  it  moreover  requires  an  examination  of  each  of 
the  individuals  separately  and  in  detail,  which  is  in 
some  cases  impossible  on  account  of  the  number,  and 
in  others  they  are  inaccessible. 

1303.  Still,  however,  in  some  branches  of  science 
this  method  is  preferable,  and  perhaps  even  indispen- 
sable. In  Botany,  in  Chemistry,  in  Anatomy, 

thod  on^  Me‘  ana  suca  hke  sciences,  which  consist  almost 
entirely  of  details,  and  in  which  there  are 
comparatively  but  very  few  general  principles  as  yet 
established,  we  must  of  course  confine  ourselves  to 
teaching  the  facts  as  they  are  known,  and  as  far  as  they 
are  known.  The  Causes  and  Laws  which  determine 
those  facts  are  as  yet  unknown  to  us,  if  not  altogether 
beyond  the  reach  of  our  faculties. 

1304.  In  the  Analytic  Method  of  Teaching,  the 
subject  of  which  we  speak  is,  of  course,  an  individual, 

Analytic  Me-  and  we  Pass  from  one  to  another  as  fast  as 
th“a  individual  we  have  predicated  of  each  what  we  know 
subject.  0f  it5  or  at  least  that  portion  of  what  we 


IV.]  METHODS  OF  INSTRUCTION  AND  CRITICISM. — SECT.  VI.  363 

know  of  it  wdiich  our  purpose  requires  us  to  com- 
municate. 

1305.  But  in  the  Synthetic  Method  we  begin  with 
the  general  subject  which  comprehends  the  Tlje  synthetic 
individuals.  We  predicate  of  it  whatever  Method- 
belongs  to  it  as  a general  subject,  then  divide  it  into 
its  coordinate  parts,  and  those  parts  again  into  their 
subordinates,  and  so  on  until  we  come  to  the  indi- 
viduals included  in  each  part. 

1306.  As  each  part  is  less  comprehensive  than  its 
whole,  and  so  on  until  we  come  to  the  indi- 
vidual, each  part  will  have  something  to  be  quires  special 
said  of  it  which  could  not  have  been  predi-  predlcall0n- 
cated  of  its  superior  and  comprehending  part  in  any 
previous  sections,  and  which  ought  to  be  predicated 
before  we  proceed  to  its  subordinates. 

1307.  These  two  Methods  differ  much  less  in  rela- 
tion to  the  fulfilment  of  the  Logical  condi- 
tions of  Method  than  would  appear  at  first  the’ffTn!thods 
sight.  There  is  but  one  way  of  forming  a not  great 
conception  of  a subject,  whether  that  subject  be  the 
general  subject  of  our  treatise  or  the  special  subject  of 
any  subordinate  chapter,  section,  or  paragraph,  even 
down  to  the  individual.  In  all  cases  we  form,  and 
must  form,  our  conceptions  by  means  of  classification. 
By  classification  also,  and  by  that  only,  can  we  com- 
municate our  conceptions  to  others.  In  the  Analytic 
Method  we  teach  by  means  of  the  natural  classifications 
which  all  make  naturally  and  necessarily  ; while  in  the 
Synthetic  we  teach  by  means  of  those  scientific  classifi- 
cations which  are  the  results  of  reflection,  and  some 
degree  at  least  of  advance  towards  the  maturity  of 
Science.* 


* For  an  illustration  take  the  following.  Suppose  a writer  treating  of 
Zoology  synthetically,  he  would  begin  by  defining  his  general  subject, 
“ animals  ; ” giving  its  Essentia  as  “ living  beings,”  its  Differentia  “ with 
material  organizations,  and  living  only  on  organic  matter,  either  vegetable 
or  animal.”  The  first  clause  limiting  against  spiritual  beings,  angels,  &e., 
and  the  second  against  the  vegetable  kingdom.  He  would  then  divide  into 


364 


LOGIC. — PART  II. 


[chap. 


1308.  Our  conception  of  an  object  may  be  analyzed 
into  its  Essentia,  Differentia,  Accidents,  Quantity  or 

Comparison,  Cause  and  Effects.  This  order 
ception  divided  is  not  in  all  its  successive  steps  strictly  neces- 

with  reference  T,  . i . i x ° 

to  the  order  of  sary.  it  is,  however,  the  most  convenient, 
communication.  rpjic  concepj-jou  js  completed  by  the  two  first, 

Essentia  and  Differentia,  in  all  that  is  essential  to  its 
completeness.  The  others  are  necessary  to  its  adequacy. 

1309.  The  Essentia  and  Differentia  give  us  all  the 
matter  which  is  necessary  to  enable  us  to  form  the 

conception  of  any  object  of  thought.  They 
and  Differentia  are,  therefore,  all  that  is  necessary  to  the 

alone  necessary  -i  * . • n liii 

for  the  a priori  adequacy  ot  the  conception  for  ail  the  pur- 
poses of  a priori  Methods  of  Investigation  or 
Proof,  as  in  the  Analysis  of  a Conception,  giving  us 
the  Matter  of  Analytic  Judgments  and  in  the  Demon- 
stration of  the  reality  of  Implied  Properties. 

1310.  But  our  conception  of  an  object  is  never  ade- 
cpiate,  nor  can  our  Science  be  completed  until  we  have 

ascertained  by  the  Methods  of  Investigation 
Quantity,  Ac  the  Accidents — including  the  separable  and 

necessary  to  the  . i -t  j 1 

conception  lbr  inseparable — and  the  Continuous  or  Discrete 
Quantity  and  its  Protensive  Relation  to  its 
antecedents  and  consequents. 

1311.  Comparison  is  by  no  means  a necessary  ele- 
ment in  the  formation  of  our  conception  of  an  object. 

It  may  serve  instead  of  Quantity.  Thus  if 
nrd0uhvaysS0"e-  the  question  be  asked,  flow  large  are  the 
evssary.  Hottentots  ? The  answer  may  be  definite 


four  “ Departments,” — Vertebrata,  Articulata,  Mollusca,  and  Radiata,  each 
department  into  Classes,  classes  into  Orders,  orders  into  Genera,  genera 
into  Species,  species  into  Varieties,  and  varieties  (the  infima  species)  into 
Individuals,  describing  each  in  its  order ; and  in  describing  the  individual 
he  would  refer  it  to  the  species,  and  thereby  in  effect  predicate  of  it  all 
that  had  been  said  of  each  subaltern  species  or  genera  up  to  the  highest.  Its 
specific  name  would  at  once  classify  and  describe  all  that  for  the  most  part 
we  care  to  know  of  it.  But  in  the  Analytic  Method  he  would  begin  with 
the  first  animal  he  might  meet.  He  would  have  to  begin  with  saying, 
“ this  dog,”  “ this  cat,”  “ this  worm,”  &c.,  as  the  case  might  be,  in  all  cases, 
however,  referring  to  the  common  and  well-known  class-names  of  the  indi- 
vidual he  might  be  examining. 


rv.]  ME'l'HODS  OF  INSTRUCTION  AND  CRITICISM. SECT.  VI.  365 

in  Quantity — '•'•four  feet  and  a half  • ” (which,  how- 
ever, is  after  all  a comparison  with  the  foot , taken  as  a 
unity  of  measure,)  or  it  may  he  by  comparison , thus, 
“ much  less  than  the  ordinary  height  of  Europeans.” 

1312.  Or  we  may  have  the  question  of  quantity  as 
to  the  comprehensiveness  of  the  sphere  of  the  concep- 
tion. Thus  in  describing  a class,  we  say  it  Quamity  of 
is  a “ large  ” or  a “ small  ” one.  Or  possi-  hheensive^0e“poef 
bly  we  give  the  precise  number  of  indivi-  the  Sphere- 
duals  included  in  it,  especially  if  the  number  be  small. 
Or  again,  we  may  give  an  idea  of  the  quantity  by 
comparison  with  another  class,  calling  it  larger  or 
smaller  than  some  other  whose  comprehensiveness  is 
known. 

1313.  There  are  many  objects  which  we  do  not 
conceive  of  as  Cause  or  as  Effect.  Thus  in 
speaking  of  a Geometrical  Figure,  we  should  feet  not  always 
not  be  likely  to  conceive  of  it  as  an  effect  rei|l“re  ' 
whose  cause  is  important  to  our  knowledge  ; nor  yet 
should  we  think  of  it  as  a cause  whose  effects  it  could 
be  important  to  investigate.  Still,  however,  the  con- 
ception of  a triangle  for  example  is  an  effect.  It  is  the 
creation  of  mind,  and  it  is  a cause ; for  it  has  stirred 
up  all  that  mental  activity  which  has  produced  the 
Sciences  of  Geometry  and  Trigonometry. 

1314.  We  come,  therefore,  to  the  Essentia  and  the 
Differentia  as  that  which  is  always  necessary  Essentia  and 
to  a distinct  and  definite  conception  of  any  wa^rentinecel- 
subject ; and  which,  therefore,  must  be  Lo-  sa,y- 
gically  first  in  all  Methods  of  Instruction,*  as  well  as 
in  all  constructions  of  systems  and  sciences.  Without 
them  there  can  be  no  conception  of  the  subject,  whe- 
ther general,  special,  or  individual. 

* It  is  often  advisable,  for  rhetorical  reasons,  not  only  to  state  the 
Differentia  in  such  positive  terms  as  connote  the  subject,  but  also  to  in- 
crease the  distinctness  of  the  outline  of  our  conception,  by  contrasting  it 
■with  its  coordinates  speaking  of  their  Differentia,  thus  fixing  the  attention 
upon  them,  and  thus  affirming  that  they  do  not  belong  to  the  class  of  objects 
of  which  we  are  speaking.  This  is  sometimes  called  defining  a subject  by 
negatives,  or  negatively — that  is,  distinctly  saying  what  it  is  not. 


366 


LOGIC. — PAKT  n. 


[chap. 


Distinct  and 
Definite  Con- 
ceptions by  Es- 
sentia and  Dif 
ferentia. 


1315.  By  the  Essentia  we  get  a distinct  concep- 
tion— the  mind  is  assured  of  a reality,  a substance, 

since  it  has  its  Constitutive  or  Material  Pro- 
perties. But  the  conception  becomes  defi- 
nite only  by  means  of  the  Differentia.  The 
Differentia  distinguish  it  from  others,  conse- 
quently defines  it,  or  fixes  the  limits  within  which  it  is 
a reality. 

We  may,  therefore,  perhaps  sum  up  the  principles 
principles  of  of  Order  in  the  Method  of  Instruction  as 
Order.  follows  : 

1316.  (1)  State  first  the  general  subject  by  its  Es- 
First  principle,  sentia  and  Differentia ; referring  always  to 
the  natural  classifications,  even  when  we  have  occa- 
sion to  use  a scientific  one.* 

1317.  (2)  Divide  it  into  coordinate  parts  or  species, 
on  the  simplest  principle  at  your  command,  and  then 

second  prin-  subdivide  as  far  as  the  case  may  require, 
cipie.  giving  to  each  coordinate  and  subordinate 

part  its  Differentia,  as  we  proceed  to  treat  each  of  the 
parts  in  the  order  and  degree  of  their  subordination. 

1318.  (3)  Whatever  subject  we  teach,  whether  the 
Third  principle,  general  or  either  of  the  subordinate  parts, 
define  it  first  by  Essentia  and  Differentia,  that  so  the 
learner  may  know  distinctly  and  definitely  what  we 
are  treating  of. 

1319.  (4)  The  order  in  which  the  other  topics,  as 
Accidents,  Quantity  or  Comparison,  and  Cause  and 

Fourth  prin-  Effect  ought  to  follow,  will  depend  upon  the 
cipie.  End  we  ]iave  in  view.  It  is  possible  that 

Quantity  is  all  that  is  desired.  It  other  cases  it  will 
be  wholly  unimportant,  and  therefore  deserving  to 


* We  are  to  remember  that  not  all  the  Peculiar  Properties  of  any  class 
are  to  he  regarded  as  its  Differentia.  The  Differentia  are  only  those  pecu- 
liar properties  which  are  most  obvious  and  conspicuous.  At  least  this  is 
always  so  in  the  Natural  Classifications.  And  much  is  added  to  the  per- 
spicuity and  vividness  with  which  instruction  is  communicated,  by  a suc- 
cessful tact  in  characterizing  the  subjects  by  those  properties  which,  while 
they  are  peculiar  and  so  determinate  of  species,  are  also  conspicuous  to  the 
observation. 


rv.]  METHODS  OF  INSTRUCTION  AND  CRITICISM. SECT.  VI.  367 

be  omitted  as  surplusage.  Again,  the  Cause  or  the 
Effect,  either  or  both,  may  be  the  only  thing  demanded, 
or  they  may  be  a matter  in  which  no  interest  is  taken, 
and  must  be  given  or  omitted  accordingly.  And  so 
among  the  Accidental  Properties  — those  must  be 
selected  which  the  object  in  view  requires,  reipember- 
ing  here  as  every  where,  that  whatever  is  not  condu- 
cive to  the  End,  is  to  be  rejected  (761).  This  is  one 
of  the  most  fundamental  principles  of  Method. 

1320.  The  mind  is  always  impatient  of  any  matter 
that  is  irrelevant  to  the  End  in  view,  and  Themmdim- 
even  of  the  intrusion  of  any  piece  of  matter 

which  is  relevant,  provided  it  be  out  of  place  ter- 
and  comes  in  before  something  else  that  is  necessary  to 
its  proper  progress.  Take  the  following  example  : — - 
“ The  Coquallin  was  sent  from  America,  by  the  name 
of  the  Orange-colored  Squirrel.  It  is,  however,  not  a 
squirrel.  It  is  a beautiful  animal,  and  very  remark- 
able for  its  color,  its  belly  being  of  a fine  yellow,  and 
its  head  as  well  as  body  varied  with  white,  black, 
brown,  and  orange ; it  covers  its  back  with  its  tail, 
like  the  squirrel,  but  has  not,  like  that  animal,  small 
brushes  of  hair  at  the  tips  of  the  ears  : it  never  climbs 
up  any  trees,  but  dwells  in  the  hollows  and  under  the 
roots  of  trees,  like  the  garden  squirrel.” 

1321.  Mow  here  after  the  assertion,  “ it  is  not  a 
squirrel,”  the  mind  was  expecting  the  Differentia  be- 
tween it  and  the  squirrel,  whereas  the  author  gives  a 
series  of  propositions,  which  so  far  from  being  Differ- 
entia of  natural  species,  may  as  well  be  applicable  to 
the  Squirrel  as  to  the  Coquallin. 

1322.  Every  body  has  observed  the  difference  in 
the  degree  of  ease  with  which  they  remember  the  writ- 
ings and  instructions  of  different  teachers. 

This  is  owing  in  a great  measure  to  the  per-  mcmkrmg  de- 
fection of  the  Method  of  the  Teacher.  He  FhodhTi^ch- 
lias  what  is  always  necessary  to  successful  In?' 
teaching,  a clear  conception  in  his  own  mind  of  the 
subject  and  of  the  snecial  end  for  which  the  instruction 


368 


LOGIC. — PART  H. 


[CHAP. 


is  at  that  time  sought,  and  upon  which  therefore  the 
interest  in  the  subject  itself  depends.  He,  therefore, 
by  the  natural  laws  which  govern  the  operation  of  his 
own  mind,  mentions  the  subject,  referring  it  to  a well 
known  Proximate  Genus,  and  then  giving  the  most 
marked  and  distinguishing  Differentia  of  its  species. 
He  carefully  excludes  all  matter  that  is  not  pertinent 
and  conducive  to  the  end  for  which  he  is  communicat- 
ing the  instruction,*  and  finally  selects  and  arranges 
whatever  he  is  to  predicate  of  his  subject  with  reference 
to  that  end. 

1323.  Rhetorically  one  of  the  first  things  for  a 
teacher  to  do  is  to  awaken  an  interest  in  his  subject, 
Fir  t awaken  ^7  fixing  in  the  mind  some  End  to  be  gained 
an  'interest  ein  by  the  instruction.  Although  this  is  a vio- 
tho  lation  of  the  principles  of  Logical  Method, 

it  is  nevertheless  so  important  to  the  rhetoric  of  in- 
struction, that  it  may  well  be  placed  in  the  rank  of  the 
highest  importance. 

1321.  The  End  must  of  course  be  sufficiently  im- 
portant to  awaken  an  interest  in  the  subject  itself,  and 
Nature  of  the  1°  excite  that  interest  to  such  a degree  of 
End-  intensity  as  to  raise  the  mind  to  a high  state 

of  activity,  and  do  away  with  the  sense  of  tediousness 
which  attends  upon  all  aimless  exertion. 

1325.  If  the  mind  were  sufficiently  capacious  to 
comprehend  all  things — all  the  properties  and  bearings 
of  any  one  subject  even — there  would  be 
omission  of  many  cases  m winch  there  could  be  no  need 
of  such  a principle  of  selection  and  omission 
as  we  have  referred  to.  But  the  mind  is  not  of  suffi- 
cient comprehension  to  receive  and  retain  all  that  we 
can  learn  or  may  desire  to  know.  This  fact  is  not  per- 
haps very  flattering.  But  it  is  well  to  have  it  distinctly 
understood  and  admitted.  It  may  humble  oar  pride 

* Quidquid  praecipies,  esto  "brevis  : ut  cito  dicta 
Percipiant  animi  dociles,  teneantque  fideles. 

Omne  supervacuum  plcno  de  pectore  manat. 

Hor.  De  Ars  Poet.  335. 


IV.]  METHODS  OF  INSTRUCTION  AND  CRITICISM. SECT.  VII.  369 

somewhat,  hut  it  will  make  us  wiser  and  teach  us  at 
an  early  day  the  necessity  of  economizing  time  and 
labor,  and  saving  ourselves  a vast  amount  of  labor  and 
toil,  which  would  otherwise  have  been  spent  in  vain. 

1326.  It  is  no  part  of  Logic  to  ascertain  the  various 
Ends  for  which  instruction  may  be  sought,  and  from 
which  we  may  derive  our  interest  in  any  subject.  The 
End  may  be  merely  and  purely  the  love  of  truth.  It 
may  be  some  immediate  practical  application  which 
we  wish  to  make  of  the  knowledge  we  are  seeking. 
But  Avithout  such  an  End  in  view,  hut  little  will  be 
sought  and  still  less,  effectually  obtained. 

SECTION  VII. 

Method  of  Logical  Criticism. 

1327.  Hitherto  in  our  discussion  of  Formulas  and 
Methods,  we  have  supposed  ourselves  occupying  a 
point  of  time  anterior  to  construction ; and 
discussing  the  Formula  and  Principles  by  view  occupied 
which  to  be  guided  in  our  work.  But  in  bythecnt,c- 
experience  it  is  quite  as  often  that  we  occupy  a differ- 
ent position,  and  have  to  perform  the  part  of  the  judge 
or  the  critic  of  that  which  has  already  been  produced 
or  constructed,  or  at  least  imagined  for  construction. 
We  wish  to  criticise  our  own  arguments  and  investiga- 
tions, theories  and  systems,  before  they  go  out  to  the 
world.  And  every  where  in  Literature  and  Necessity  for 
Science  we  meet  with  the  like  productions  Criticism- 

of  other  minds  which  need  to  be  thus  examined  and 
criticised,  as  a part  of  the  process  by  which  they  can 
become  our  own  or  in  any  way  profitable  to  us. 

1328.  It  is  obvious  that  the  Formula}  and  Principles 
must  be  precisely  the  same  for  Criticism  as  principles  of 
for  Construction.  And  so  far  as  the  Method  ^cis“  thtb® 
of  Criticism  is  determined  by  the  Idea  of  the  °f  construction. 
True,  nothing  further  need  be  said  than  is  contained  in 
the  preceding  pages.  It  is  immaterial  in  what  way  or 

16* 


370 


LOGIC. — PART  II. 


[CHAP. 


order  we  apply  these  principles,  if  so  be  that  we  apply 
them  and  find  the  conformity  or  want  of  conformity  to 
them  in  what  comes  under  our  notice.  What  we  shall 
its  Methods,  have  to  say  further  of  the  Method  of  Criti- 
cisms, therefore,  will  be  determined  by  the  Idea  of  the 
Useful,  as  giving  the  readiest  and  quickest  way  of  ac- 
complishing the  result. 

1329.  In  order  to  a successful  and  scientific  Criti- 
cism, the  first  and  indispensable  step  is  to  get  an  ade- 

idea  of  the  Tuate  idea  01’  conception  of  the  work  to  be 
whole  the  start6-  criticised,  as  a whole,  its  structure  and  its 
aim.  For  in  most  cases  we  cannot  get  at 
the  parts  to  form  any  conception  of  them,  and  criticise 
them  without  first  analyzing  the  whole,  that  we  may 
thereby  discover  what  are  its  parts.  But  more  than 
this  an  adequate  conception  of  a part  can  never  be 
formed  without  considering  its  relation  to  the  whole 
The  necessity  as  a constituent  part  of  it.  Considered  as  a 
font.  whole  and  absolutely,  many  a subject  of  our 

criticisms  may  be  faultless,  while  yet  it  has  no  value 
or  adaptation  if  considered  relatively  to  its  whole  ; and 
vice  versa,  parts  that  are  faultless  in  reference  to  their 
comprehending  wholes,  are  without  comeliness  and 
meaning,  considered  by  themselves. 

1330.  Wholes  are  never  a mere  accumulation  or 
generalization  of  the  parts.  They  are  rather  collective 

The  whole  not  generaT  Many  things  may  be  predi- 

a mbe  general  cated  of  them  which  cannot  be  predicated 

Conception.  , -i  j • l xiii 

ox  any  one  oi  the  contained  or  comprehended 
parts.  Much,  for  example,  can  be  said  of  man  as  a 
living  whole,  which  could  not  be  predicated  of  any  of 
the  parts  into  which  Anatomy,  Chemistry,  or  even 
Metaphysical  Analysis  can  resolve  him.  It  is  so  of  all 
wholes,  and  hence  the  necessity  of  examining  and  cri- 
ticising them  as  wholes  over  and  above  any  examina- 
tion or  criticism  which  we  may  give  to  their  component 
parts. 

1331.  This  fault  of  judging  of  parts  as  wholes  and 
not  as  parts  merely,  or  in  their  relation  to  the  whole, 


IH.]  METHODS  OF  INSTRUCTION  AND  CRITICISM. SECT.  VII.  371 

Whately  has  referred  to  the  Fallacy  of  Division  and 
Composition.  It  is,  however,  no  Fallacy  in  Form. 
It  is  a Fault  of  Method  originating  in  a want  of  com- 
prehensiveness of  views.  I have  already  quoted 
Wliately’s  language  in  regard  to  it  (749).  To  take  his 
example : “ The  spendthrift  compares  his  in-  T1?e  gpend. 
come  with  each  particular  item  as  a whole,  thrilt  s Fault' 
and  finds  it  small  compared  with  what  he  has  to  ex- 
pend— five  dollars  for  an  evening’s  amusement  out  of 
an  income  of  a thousand  ! It  is  certainly  inconsider- 
able. Such  a sum  cannot  ruin  any  body.  It  is  mere 
niggardliness  not  to  afford  it.”  But  considered  as  a 
part  of  the  annual  expenditure  it  may,  after  all,  be 
found  to  be  just  the  sum  and  the  item  which  will 
leave  one  in  arrears  at  the  end  of  his  financial  year. 
The  same  fault  is  often  committed  by  persons  in  mak- 
ing their  estimate  of  their  own  character  and  abilities. 
Hot  considering  that  one  or  two  acts  are  sufficient  in 
some  cases  to  determine  the  character,  they  form  quite 
a different  estimate  of  themselves  from  that  which  their 
neighbors  have  formed.  One  or  two  acts  of  fraud,  of 
intemperance,  of  intentional  deception,  destroy  entirely 
one’s  character  for  honesty,  temperance,  and  veracity. 
So,  too,  although  it  be  true  that  “ the  best  fail  some- 
times,” yet  frequent  failures  to  meet  our  engagements, 
or  to  perform  the  duties  required  or  expected  of  us 
from  our  position,  is  ruinous  to  one’s  character  for 
capacity  or  competency  to  the  duties  and  responsibili- 
ties of  his  position.* 

* It  is  often  a successful  trick  of  Sophistry  to  criticise  what  are  called 
“ the  Points  ” of  an  Argument,  as  if  they  were  wholes  ; that  is,  Arguments 
each  complete  in  itself,  obstinately  and  artfully  keeping  out  of  view  and  out 
of  consideration  the  fact  that  they  are  hut  parts  of  a cumulative  whole.  In 
this  way  the  force  of  any  Argument  from  circumstantial  testimony  or  cumt 
lative  Argument  of  any  kind,  may  be  shown  to  have  little  or  no  force. 
The  Method  is  no  less  absurd  than  would  be  the  attempt  to  estimate  the 
strength  of  an  arch  by  ascertaining  how  much  each  stone  taken  separately 
would  sustain,  and  then  taking  the  aggregate  as  indicative  of  the  strength 
of  the  whole  arch ; when  in  fact  more  than  one-half  of  the  stones,  per- 
haps, not  only  would  not  sustain  any  thing  in  their  position,  hut  need  to  be 
supported  by  thoso  below  them  to  keep  them  from  falling. 


372 


LOGIC. PAKT  II. 


[ciiap. 


1332.  What  are  to  be  regarded  as  wholes  and  what 
as  parts,  is  determined  by  the  choice  of  the  mind  from 

whole,  i which  they  emanate  ; and  the  same  thing 
what  dciermiio  may  be  regarded  as  a part  or  as  a whole,  j list 
as  in  the  use  which  has  been  made  of  it 
in  the  case  under  consideration  it  was  designed  for  a 
whole  in  itself,  or  to  serve  as  a part  to  a larger  whole 
and  a means  to  an  end  not  contained  in  itself.  Thus 
a Treatise  on  the  Evidences  of  Christianity  may  be 
planned  and  executed  as  a whole,  to  be  complete  in 
itself;  or  it  may  be  planned  and  written  with  reference 
to  a particular  end,  to  serve,  for  instance,  as  an  intro- 
The  same  thing  duction  to  a Treatise  on  Christian  Ethics,  or 
whoeie'&sSomea  as  a part  of  a system  of  Theology.  A volume 
times  a part.  on  Algebra  may  be  designed  to  be  complete 
as  a whole,  or  only  to  serve  as  a part  of  a series  on 
Mathematics  ; and  it  will  be  modified  in  its  plan  and 
in  its  execution,  according  as  it  is  to  be  a whole  or  a 
part,  and  will  of  course  require  to  be  criticised  and 
judged  by  different  rules,  as  it  is  to  be  regarded  from 
the  one  or  the  other  of  these  points  of  view. 

1333.  Wholes  are  to  be  criticised  chiefly  with  a 
view  to  the  Principles  of  Method,  the  Methods  by 

pans  to  be  which  they  are  constructed.  We  may, 
t°esidc$leism  °f  course,  have  them  as  Investigations  or 
or  wholes.  Inquiries  as  they  are  sometimes  called,  as 

Arguments,  or  as  Scientific  Systems.  And  in  con 
sidering  the  Methods  the  points  to  which  our  attention 
is  to  be  chiefly  directed,  are  (1)  the  End  or  Aim  to  be 
accomplished  ; (2)  the  compatibility  of  the  End  with 
the  Matter  in  which  it  is  to  be  accomplished  ; and 
(3)  the  adaptation  of  the  Method  to  the  Matter  and  the 
End.  For  example,  we  cannot  produce  the  absolute 
certainty  of  demonstration  in  Moral  Matter,  or  by 
means  of  Testimony.  Nor  would  it  be  in  accordance 
with  the  Principles  of  Method  to  prove  a proposition  in 
Geometry  by  an  induction  of  facts,  or  a doctrine  of 
Revelation  by  means  of  the  opinions  of  uninspired 
men. 


IV.]  METHODS  OF  INSTRUCTION  AND  CRITICISM. SECT.  VH.  373 

1334.  We  are  not  to  suppose  that  the  whole  of  any 
hook  or  treatise  designed  to  convince  or  persuade,  can 
he  reduced  to  any  Logical  Formula,  or  will  Not  aii  of  books 
fulfil  the  conditions  of  any  Method  of  Proof  SSofLo8 
or  Refutation.  Much  is  often  thrown  in  for  g,cal  CritJCI3m' 
embellishment  addressed  to  the  Fancy,  and  much  is 
designed  merely  to  make  an  impression  upon  the  sen- 
sibilities and  feelings  either  in  favor  of  or  against  the 
main  conclusion  ; and  some  whole  hooks  have  no  other 
object  than  to  please  or  amuse,  or  to  make  an  impression 
upon  the  feelings  without  convincing  the  reason.  Even 
books  designed  to  convey  instruction  do  not  necessarily 
contain  much  or  even  any  argument.  They  may  be  oc 
cupied  with  stating  facts  alone,  from  which  no  conclu- 
sion is  designed  to  be  drawn. 

1335.  An  impression  made  by  a description,  a nar- 
rative, a sarcasm,  or  a jeer,  may  often  be  a more 
efficient  motive  of  action  than  a conviction 

of  the  understanding  produced  by  facts  and  upon  the  sensi- 

. t>  , x ^ -i  bilities  more 

reasoning.  Rut  these  impressions,  unless  effective  than 
under  the  control  of  the  Conscience  and  Arguments- 
Reason,  are  always  in  danger  of  misleading  us.  They 
are  not,  however,  Fallacies.  We  cannot  reduce  them 
to  Logical  Formulae.  We  can  meet  them  for  the  most 
part  by  arguments  addressed  to  the  Reason,  designed 
to  show  that  the  course  to  which  the  impression  would 
lead  us  is  wrong.  Yet  it  is  probable  that  the  largest 
part  of'  mankind  are  governed  and  guided  more  by 
their  impressions  than  by  their  convictions.  Convic- 
tions alone,  however,  belong  to  the  sphere  of  Logic 
and  of  Reasoning  — Impressions  and  Persuasion  to 
Rhetoric. 

1336.  It  is  the  right  and  privilege  of  the  framer  of 
an  argument  to  introduce  whatever  terms,  and  to  put 
them  in  whatever  relation  to  each  other  he  No  new  mat. 
may  choose.  W e may  introduce  no  new  ^odS be  ?n 
ones  in  completing  the  Formula,  and  if  he  Praxis- 

has  not  given  us  material  enough  to  complete  the  For- 
mula, the  responsibility  of  the  failure  must  be  his. 


LOGIC. — PART  n. 


374 


[chap. 


His  language  must  be  regarded  as  mere  declamation, 
unfounded  assertion,  vox  et  prceterea  nihil. 

1337.  And  here,  I take  it,  is  the  distinction  between 
argument  and  mere  assertion.  The  former  contains 
Distinction  be-  that  is  necessary  to  complete  the  Formula 
meentn  an/ls-  under  the  rules  already  given,  so  as  to  satisfy 
sertion.  the  mind  completely  what  are  the  grounds 
upon  which  the  speaker  or  writer  would  rest  his  con- 
clusions. But  from  mere  assertion  no  form  of  a com- 
plete argument  can  be  made  out  without  introducing 
new  matter ; and  this  would  throw  the  responsibility 
for  the  Argument  upon  the  critic  who  completes  it, 
rather  than  upon  the  author  who  should  have  given  it 
already  completed. 

1338.  But  besides  all  that  is  addressed  merely  to 
the  fancy  and  the  feelings,  all  that  is  intended  as  mere 

instruction  to  be  received  on  authority  of  the 
gumects6"  and  teacher,  and  all  that  is  mere  declamation, 

mere  Artifices.  i j • i j i 

there  are  also  the  artifices  or  tricks  to  be 
separated  from  what  properly  comes  within  the  sphere 
of  Logic.  These  tricks  have  already  been  defined  (753), 
and  discriminated  from  Faults  or  Fallacies.  They  have 
not  been  enumerated ; for  no  diligence  could  collect, 
classify,  and  describe  all  the  artifices  of  this  kind  which 
carelessness  may  let  fall  or  cunning  devise.*  Sagacity 
and  constant  watchfulness  alone  can  guard  one  against 
falling  into  them  himself,  or  being  entrapped  by  them 
when  dealing  with  the  unscrupulous  and  designing. 

1339.  The  first  step,  therefore,  towards  a Logical 
Analysis  of  any  work  is  to  discriminate  the  Thought 
from  the  Rhetoric,  to  select  all  that  belongs  to  the  pro- 
vince of  reasoning  and  intelligence,  from  that  which  is 
mere  Trick  or  Artifice — gaseous  declamation,  or  mere 
didactic  development  of  Premises. 

1340.  In  criticising  the  Terms  it  will  be  necessary 
to  consider  whether  they  are  properly  used  or  not,  and 

* “ Quas  aut  incuria  fudit 
Aut  humana  parum  cavit  natura.”—  Hok. 


IV.]  METHODS  OF  INSTRUCTION  AND  CRITICISM. SECT.  VII.  375 

whether  a word  may  not  be  improperly  used  to  express 
a cognition,  which  is  after  all  just  the  one  criticism  of 
which  is  required.  And  if  the  Term  be  com-  Terms- 
plex  we  are  to  consider  whether  the  Modals  and  the 
Term  are  not  incompatible ; as  for  example,  “ trian- 
gular ellipse.”  Or  to  give  some  illustrations  from  a 
book  that  is  before  me,  the  author  speaks  of  “ the  sub- 
stantiality of  motion,”  “ absolute  relativity,”  “ ab- 
stractly extended  subsistence.”  It  is  impos-  contmdictio 
sible  to  form  any  conception  of  what  is  inadJecti» 
meant  (if  any  thing  is  really  meant)  by  such  terms. 
This  Fault  of  Terms  has  been  called  a Contmdictio  in 
adjectis. 

1341.  In  the  criticism  of  Arguments,  it  will  be 
necessary  to  identify  in  the  first  place  the  Conclusion 
aimed  at,  since  this  determines  the  whole 

with  reference  to  which  all  the  parts,  as  whiles  of  Ard 
Terms,  Premises,  &c.,  are  to  be  criticised,  mined  by  the 
and  in  the  next  place  to  identify  the  subject  tonclusion- 
of  the  Conclusion  as  that  which  determines  the  unity 
of  the  Formula.  By  means  of  the  Subject  and  Predi- 
cate of  the  Conclusion  as  Minor  and  Major  Terms,  we 
are  to  identify  the  other  parts  of  the  Formula.  In 
doing  this  we  shall,  of  course,  find  all  of  the  principles 
and  statements  of  the  preceding  work  called  into  requi- 
sition. And  I trust  that  it  will  be  found  that  nothing 
is  required  which  is  not  contained  more  or  less  expli- 
citly and  fully  in  these  pages.  If  any  thing  more  is 
required,  the  fact  will  serve  to  show  how  far  this  Trea- 
tise is  from  being  complete. 

1342.  In  the  Methods  of  Investigation  and  of  In- 
struction the  unity  of  the  End  or  Object  will  determine 
for  us  what  are  to  be  regarded  as  Wholes,  and  -wholes  and 
of  course  by  the  same  means  what  are  to  be  ^0nn  Inand 
regarded  as  subordinate  Parts.  The  means  d?Snedonby 
to  any  End  are  always  the  parts  of  any  Me-  theEnduivlew- 
thod  to  that  End.  The  End  of  an  Investigation  is  the 
attainment  of  the  Predicate  which  we  are  investigat- 
ing. The  End  of  a Construction  is  to  put  our  thoughts 


376 


LOGIC. PART  n. 


[chap.  rv. 


into  such  form  and  order  as  to  be  communicable  to 
others.  To  this  End,  division  of  the  Subject,  order  in 
arranging,  definition  and  description,  and  each  part  of 
the  division — the  order,  the  definitions,  descriptions, 
comparisons,  and  whatever  else  we  may  have  occasion 
to  use,  are  Parts,  and  should  be  judged  as  Parts,  sub- 
ordinate and  conducive,  according  to  the  rules  and 
principles  already  discussed  ; and  whether  faultless  or 
faulty  in  themselves,  they  are  each  to  be  approved  or 
condemned,  according  as  they  shall  be  found  conducive 
to  that  End  or  not ; always  remembering  that  whatever 
does  not  conduce  to  the  End  which  is  most  promi- 
nently before  the  mind,  and  help  on  towards  its  attain- 
ment, is  a fault,  a hindrance,  and  an  annoyance. 


APPENDIX. 


EXAMPLES  FOR  ANALYSIS  AND'  CRITICISM. 

§ 1.  Of  the  order  in  criticising  Arguments. 

In  analyzing  and  criticising  the  following  Examples,  which 
have  been  selected  with  a special  view  to  illustrate  the  Prin- 
ciples and  Formulae  of  the  foregoing  Treatise,  we  shall  find 
the  following  order  useful  as  expediting  the  process. 

In  the  first  place,  in  each  unity  or  totality  of  an  Argument 
we  must  ascertain  what  is  the  point  to  be  proved — the  Con- 
clusion of  the  Argument  as  a Whole.  This  is  necessary  at 
this  stage.  For  by  this  only  can  we  identify  the  Minor  and 
Major  Terms — the  Subject  of  the  Argument,  and  what  is 
proved  of  it.  And  it  is  only  by  this  process  of  identifying  the 
Subject  and  Predicate  of  the  Argument  that  we  can  identify 
the  Premises,  and  ascertain  their  character  and  position. 

Having  identified  the  Minor,  Middle,  and  Major  Terms  by 
means  of  the  Subject  and  Predicate  of  the  Conclusion,  we  can 
next  identify  the  Premises,  and  arrange  the  Matter  of  the 
Argument  into  its  appropriate  Formula,  and  complete  the 
Formula  if  it  should  require  completing. 

And  as  soon  as  we  have  done  this,  we  shall  find  an  advan- 
tage in  disconnecting  the  Matter  from  the  Form,  by  substitut- 
ing in  the  Formula  some  one  of  the  Letters  of  the  Alphabet. 
We  derive  the  same  advantage  in  Logical  Analysis  as  in 
Algebra,  from  using  the  symbolical  letters  for  the  sums  and 
quantities  which  they  represent.  It  facilitates  the  process,  and 


378 


LOGIC. — APPENDIX. 


errors  are  less  likely  to  be  made,  and  are  more  easily  detected 
if  they  are. 

In  the  next  place  we  are  to  consider  if  there  is  any  Fault 
or  Fallacy  in  the  general  form  or  argument.  It  will  always 
be  best  to  look  for  them  in  the  following  order : 

(1)  An  Ignoratio  Elenchi. 

(2)  Any  Fault  in  Form  or  in  Method. 

(3)  Any  Fallacy  in  Matter  or  in  Diction. 

If  either  of  these  defects  is  found,  the  work,  whatever  other 
excellencies  and  attractions  it  may  have,  is  worthless  as  an 
Argument,  or  effort  to  sustain  the  truth  of  its  Conclusion. 

The  next  step,  after  having  selected  and  arranged  the  parts 
of  the  main  Argument,  is  to  separate  each  of  the  subordinate 
parts  into  logical  wholes  or  unities ; remembering  always  that 
the  unity  of  the  Argument  or  Formula  consists  in  the  unity 
of  its  Subject. 

Having  thus  divided  the  work  up  into  its  smallest  parts 
that  can  be  regarded  as  wholes  at  all,  we  are  to  proceed  to 
reduce  them  to  the  Formulae.* 

The  first  thing  here  is  to  identify  the  Conclusion,  and  from 
the  Conclusion  the  Terms,  Minor  and  Major,  which  are  given 
in  it.  We  are  also  to  notice  whether  it  be  simple,  complex, 
or  compound ; and  what  is  the  complicity  of  the  judgment  of 
which  it  is  compounded,  with  reference  to  its  including  any 
thing  illicit,  by  this  means. 

We  may  here  consider  whether  there  be  any  Ignoratio 
Elenchi,  or  Fault  in  Method  in  this  part  of  the  main  argu- 
ment, or  not ; for  if  there  is,  we  need  go  no  farther  in  our 
analysis  of  this  part,  since  though  it  should  be  otherwise  fault- 
less, it  is  nothing  to  the  purpose. 

We  are  next  to  identify  the  Premises  by  means  of  the 
Terms  which  we  have  found  in  the  Conclusion ; note  their 
Relation,  as  whether  Categorical,  Conditional,  or  Disjunctive. 
Then  put  the  elements  thus  given  into  the  Formal  position, 
and  complete  the  Formula  if  it  be  not  complete. 

* Most  of  the  Scholastic  Writers  on  Logic  whose  works  I have  seen, 
speak  of  two  kinds  of  Syllogisms,  Formal  and  Material ; the  Material  Syl- 
logisms are  those  which  contain  all  the  Matter  of  a Syllogism,  but  not 
stated  in  any  recognized  Formula.  A Formal  Syllogism  is  an  argument 
stated  in  a recognized  Formula.  The  business  of  Praxis  is,  therefore,  to 
reduce  Material  to  Formal  Syllogisms. 


EXAMPLES  FOR  CRITICISM. 


379 


In  the  course  of  this  completion,  we  are  not  only  to  find 
the  supposed  or  assumed  Premises  in  Enthymemes  of  the  various 
forms,  but  also  the  Sequence  in  Conditionals,  the  Excluded 
Middle  in  Disjunctives,  and  the  identity  of  kind  in  things 
compared.* 

Having  completed  the  Formula,  we  are  next  to  consider  it 
in  relation  to  the  Faults  and  Fallacies  in  the  order  above 
given. 

If  we  find  the  part  of  the  main  argument  which  is  under 
examination  inconclusive  for  any  reason,  we  are  next  to  con- 
sider how  important  it  is  as  a part  of  the  main  argument. 
And  whether  a failure  or  not,  we  are  carefully  to  estimate  its 
value  and  its  force,  if  it  has  any,  as  a means  of  establishing  the 
main  Conclusion.  We  shall  find  the  Conclusion  either  a Pre- 
mise in  the  main  Argument,  or  the  assertion  of  a fact  which  is 
used  by  way  of  Induction,  Analogy,  Example,  or  Circum- 
stance, &c.,  to  prove  a Conclusion  which  is  used  as  such  a 
Premise. 

In  this  way  we  are  to  analyze  each  subordinate  part  of  the 
main  Argument,  taking  as  an  ultimate  part  or  unity  of  argu- 
ment only  those  which  have  but  one  subject,  and  which  there- 
fore, as  arguments , can  be  resolved  no  farther. 


§ 2.  Examples  in  Categorical  Syllogisms. 

1.  Every  effect  must  have  had  an  adequate  cause — the 
creation  of  the  world  is  an  effect ; therefore  the  creation  of  the 
world  must  have  had  a cause. 

2.  He  that  is  always  in  fear  cannot  be  happy.  But  those 
that  are  conscious  of  guilt  are  always  in  fear ; therefore  those 
that  are  conscious  of  guilt  cannot  be  happy. 

3.  Satire  is  a legitimate  mode  of  exposing  the  failings  of 
others.  But  the  calling  others  by  ill-names  is  not  satire ; 
therefore  it  is  no  legitimate  mode  of  exposing  their  failings. 

* As  it  is  convenient  to  have  a name  for  this  fault,  of  passing  from  one 
species  to  another  improperly  (for  it  is  one  of  frequent  occurrence),  we  may 
call  it  Metabasis.  This,  if  I understand  him  rightly,  is  what  Aristotle 
means  when  he  speaks  of  “ passing  over  into  another  species  : ” MerdPuais 
(is  to  &A\o  y(vos. 


380 


LOGIC. APPENDIX. 


4.  Tyranny  is  an  unnecessary  restraint  upon  human  liberty. 
The  English  government  imposes  no  unnecessary  restraint 
upon  the  liberty  of  its  subjects  ; therefore  the  English  govern- 
ment is  no  tyranny. 

5.  No  one  is  free  who  is  enslaved  by  his  appetites.  The 
sensualist  is  enslaved  by  his  appetites  ; therefore  no  sensualist 
is  free. 

6.  All  accountable  beings  are  free  agents.  Men  are  ac- 
countable ; therefore  they  are  free  agents. 

serpetual  gratification  without 


sires  what  can  never  be  attained. 

8.  That  which  has  no  reality  of  being  cannot,  as  cause, 
produce  or  be  the  ground  of  existence  to  any  thing.  Chance 
has  no  reality  of  being;  therefore  nothing  can  be  properly 
ascribed  to  chance  by  way  of  accounting  for  its  origin. 

9.  Liberality  is  a means  of  making  others  happy.  But  it 
is  not  a means  of  making  one’s  self  rich ; therefore  making 
one’s  self  rich  does  not  always  make  others  happy. 

10.  Murderers  never  escape  punishment.  Yet  even  mur- 
derers hope  to  elude  the  laws  of  their  country  ; therefore  some 
who  hope  to  elude  the  laws  of  their  country  do  not  escape 
punishment. 

11.  All  amiable  men  merit  the  esteem  and  respect  of  their 
fellow  men.  And  certainly  all  who  aim  only  to  do  good  to 
their  fellow  meD,  deserve  to  be  esteemed  and  respected  on  that 
account.  Hence  all  who  are  striving  to  do  good  to  others  are 
amiable  men. 

12.  Some  effectual  check  to  the  progress  of  seditious  pub- 
lications is  absolutely  essential  to  the  safety  of  our  country. 
The  total  abolition  of  the  art  of  printing  would  prove  such  a 
check ; therefore  the  art  of  printing  should  be  totally  abol- 
ished. 

13.  No  one  is  rich  who  has  not  enough.  No  miser  has 
enough  ; therefore  no  miser  is  rich. 

14.  The  things  that  cannot  be  enumerated  do  not  exist. 
Innate  ideas  cannot  be  be  enumerated ; therefore  there  are 
no  innate  ideas. 


therefore  the  sensualist  de- 


EXAMPLES  FOE  CEITICISM. 


381 


15.  Some  poisons  are  vegetable.  But  no  poisons  are  use- 
ful drugs  ; therefore  some  useful  drugs  are  not  vegetable. 

16.  Some  recreations  are  necessary  to  the  preservation  of 
health  and  spirits.  All  recreations,  however,  are  liable  to  be 
carried  to  excess  and  be  abused ; so  that  some  things  liable  to 
abuse  are  nevertheless  necessary  for  man. 

17.  No  tale-bearer  is  worthy  of  confidence.  But  all  tale- 
bearers are  great  talkers ; therefore  great  talkers  are  never 
worthy  of  confidence. 

18.  That  one  who  has  been  accustomed  to  liberty  can 
never  be  happy  in  the  condition  of  a slave  is  indeed  true. 
But  the  negroes  on  our  Southern  plantations  have  never  been 
accustomed  to  liberty.  Hence  they  are  content  and  happy  in 
their  present  condition. 

19.  “ He  that  is  of  Hod  heareth  my  words ; ye  therefore 
hear  them  not,  because  ye  are  not  of  God.” 

20.  All  the  most  bitter  persecutions  have  been  religious 
persecutions.  Among  the  most  bitter  persecutions  were  those 
which  occurred  in  France  during  the  French  Revolution. 
Consequently  they  must  have  been  religious  persecutions. 

21.  That  man  is  independent  of  the  caprices  of  Fortune 
who  places  his  chief  happiness  in  moral  and  intellectual  excel- 
lence. A true  philosopher  is  independent  of  the  caprices  of 
Fortune ; therefore  a true  philosopher  is  one  who  places  his 
chief  happiness  in  moral  and  intellectual  excellence. 

22.  Of  two  evils  the  less  is  to  be  preferred ; therefore 
since  occasional  turbulence  is  a less  evil  than  a rigid  despotism, 
it  is  to  be  preferred. 

23.  Some  objects  of  great  beauty  answer  no  other  percep- 
tible purpose  but  to  gratify  the  sight : many  flowers  have 
great  beauty ; and  many  of  them  accordingly  answer  no  other 
purpose  but  to  gratify  the  sight. 

24.  A man  who  deliberately  devotes  himself  to  a life  of 
sensuality  is  deserving  of  strong  reprobation ; but  those  do  not 
deliberately  devote  themselves  to  a life  of  sensuality  who  are 
hurried  into  excess  by  the  impulse  of  the  passions  : such  there- 
fore as  are  hurried  into  excess  by  the  impulse  of  the  passions 
are  not  deserving  of  strong  reprobation. 


382 


LOGIC. APPENDIX. 


25.  It  is  a difficult  task  to  restrain  all  inordinate  desires  : 

to  conform  to  the  precepts  of  Scripture  implies  a restraint  of 
all  inordinate  desires ; therefore  it  is  a difficult  task  to  conform 
to  the  precepts  of  Scripture.  * 

26.  Any  one  who  is  candid  will  refrain  from  condemning  a 
book  without  reading  it : some  Reviewers  do  not  refrain  from 
this ; therefore  some  Reviewers  are  not  candid. 

27.  My  hand  touches  the  pen,  the  pen  touches  the  paper  ; 
therefore  my  hand  touches  the  paper. 

28.  Lias  lies  above  red  sandstone,  red  sandstone  lies  above 
coal ; therefore  lias  lies  above  coal. 

29.  A true  prophecy  coincides  precisely  with  all  the  cir- 
cumstances of  such  events  as  could  not  be  conjectured  by 
natural  reason.  This  is  the  case  with  the  prophecies  concern- 
ing the  Messiah  in  the  Old  Testament ; hence  these  prophecies 
are  true. 

30.  All  that  glitters  is  not  gold : tinsel  glitters ; therefore 
it  is  not  gold. 

31.  No  trifling  business  will  enrich  those  that  engage  in  it. 
A speculation  is  no  trifling  business ; therefore  speculation  will 
enrich  all  who  are  engaged  in  it. 

§ 3.  Examples  in  the  Hypothetical  Formulae. 

32.  If  some  fishes  have  no  teeth,  some  animals  without 
teeth  are  fishes. 

33.  If  some  who  are  very  sentimental  are  nevertheless  not 
benevolent,  then  some  who  are  not  benevolent  are  sentimental. 

34.  If  fire  may  be  separated  from  a flint,  a property  may 
be  separated  from  its  subject : but  fire  cannot  be  separated 
from  the  flint ; therefore  a property  cannot  be  separated  from 
its  subject. 

35.  If  hatred  and  malice  are  contrary  to  the  Divine  law, 
they  ought  to  be  avoided  : that  they  are  so  no  one  can  deny ; 
therefore  they  should  be  avoided. 

36.  If  the  penal  laws  against  the  Papists  were  enforced, 
they  would  be  oppressed  and  wronged.  But  those  laws  are 


EXAMPLES  FOR  CRITICISM. 


383 


not  enforced,  and  therefor**  they  have  nothing  to  complain  of 
in  the  way  of  oppression  or  persecution. 

37.  If  testimony  to  miracles  is  to  be  admitted,  the  miracles 
claimed  for  Mahomet  are  to  be  admitted.  But  as  the  narrative 
of  those  miracles  cannot  be  admitted,  no  testimony  to  mira- 
cles is  to  be  admitted. 

38.  If  the  exercise  of  war  in  defence  of  one’s  country  were 
sinful,  it  would  have  been  forbidden  in  the  Scripture,  either 
expressly  or  by  implication.  But  it  is  not  so  forbidden ; 
therefore  we  may  safely  infer  that  defensive  wars  are  not 
sinful. 

39.  If  the  fourth  commandment  is  obligatory,  we  are 
indeed  bound  to  set  apart  one  day  in  seven.  But  no  one  sup- 
poses now  that  that  commandment  is  obligatory.  Hence  there 
is  no  obligation  to  keep  one  day  any  more  sacred  than  an- 
other. 

40.  Romanism  is  that  form  of  religion  which  has  the  most 
forms : and  if  forms  are  necessary  to  religion,  then  that  religion 
which  has  the  most  forms  is  the  best,  and  we  ought  all  to  turn 
Romanists. 

41.  The  adoration  of  images  is  forbidden  to  Christians  if 
the  Mosaic  law  was  designed,  not  for  Israelites  alone,  but  for 
all  men.  It  was,  however,  designed  for  Israelites  alone ; hence 
the  adoration  of  images  is  not  forbidden  to  Christians. 

42.  A wise  lawgiver  must  either  recognize  the  rewards  and 
punishments  of  a future  state,  or  he  must  be  able  to  appeal  to 
a Providence  dispensing  them  in  this  life.  Moses  did  not  do 
the  former,  and  therefore  he  must  have  done  the  latter. 

43.  The  virtues  are  either  passions,  faculties,  or  habits. 
But  they  are  not  passions  : for  passions  do  not  depend  on  pre- 
vious determination.  And  they  are  not  faculties  : for  faculties 
are  possessed  by  nature.  The  virtues,  therefore,  are  habits 
acquired  by  voluntary  exertion  and  effort. 

44.  The  early  assignment  of  the  Epistle  to  the  Hebrews 
to  St.  Paul  as  its  author,  must  have  been  either  from  its  being 
really  his,  or  from  its  professing  to  be  his  and  containing  his 
name.  But  it  makes  no  claim  to  being  his.  Consequently, 
nothing  but  a knowledge  of  the  fact  that  he  wrote  it  could 
have  led  the  early  Christians  to  attribute  it  to  him. 


384 


LOGIC. APPENDIX. 


45.  If  the  everlasting  favor  of  God  is  not  bestowed  at  ran- 
dom, and  on  no  principle  at  all,  it  must  be  bestowed  either  with 
respect  to  men’s  persons,  or  with  respect  to  their  conduct : 
but  “ God  is  no  respecter  of  persons ; ” therefore  his  favor 
must  be  bestowed  with  respect  to  men’s  conduct. 

46.  If  every  objection  that  can  be  urged  would  justify  a 
change  of  established  laws,  no  laws  could  reasonably  be  main- 
tained. But  some  laws  can  be  reasonably  maintained;  there- 
fore no  objection  that  can  be  urged  will  justify  a change  in 
established  laws. 

47.  If  any  complete  theory  could  be  framed  to  explain  the 
establishment  of  Christianity  by  human  causes,  such  a theory 
would  have  been  propounded  before  this  time.  But  no  such 
theory  has  been  proposed  ; therefore  we  may  conclude  that  no 
such  theory  can  be  devised. 

48.  If  a man  is  ignorant  he  should  consult  others  as  a 
means  of  making  up  his  deficiency  in  knowledge.  If  he  is 
wise,  yet  two  heads  for  counsel  are  better  than  one ; therefore 
in  all  important  matters  one  should  take  counsel  with  others. 

49.  If  one  is  superior  to  others  he  should  be  polite  and 
gentle  in  his  manners  towards  them,  as  a matter  of  Christian 
compassion  and  magnanimous  condescension.  If  he  is  among 
equals  he  should  be  civil  and  courteous,  since  such  a demeanor 
is  as  much  their  right  from  him  and  his  right  from  them.  And 
if  he  is  among  his  superiors,  he  should  show  himself  courteous 
and  civil,  as  being  due  to  those  having  authority  over  us  for 
the  good  of  the  whole.  In  any  case,  therefore,  we  are  bound 
by  the  most  sacred  obligations  to  be  civil  and  considerate  of 
the  feelings  of  others. 

50.  If  the  Government  provides  for  these  debts  by  impo- 
sition, it  will  become  odious  to  the  people  and  perish.  If  it 
does  not  provide  for  them,  it  will  be  overthrown  by  the  most 
dangerous  of  all  parties,  I mean  extensive  discontent  of  the 
moneyed  interest. 

51.  If  I am  under  the  chastening  hand  of  God,  and  if  there 
is  no  unrighteousness  in  Him,  it  must  be  that  I am  punished 
for  my  iniquity. 

52.  If  virtue  is  voluntary,  vice  is  voluntary.  But  virtue 
is  voluntary ; therefore  so  is  vice. 


EXAMPLES  FOR  CRITICISM. 


385 


53.  If  expiatory  sacrifices  were  divinely  appointed  before 
the  Mosaic  law,  they  must  have  been  expiatory  not  of  ceremo- 
nial sin  (for  there  could  be  none  then),  but  of  moral  sin.  If 
so,  the  Levitical  sacrifices  must  have  had  no  less  efficacy.  In 
that  case  the  atonements  under  the  Mosaic  law  would  have 
‘ made  the  comers  thereunto  perfect,  as  pertaining  to  the  con- 
science.’ But  this  they  could  not  accomplish.  Hence  we 
infer  that  expiatory  sacrifices  could  not  have  been  appointed 
before  the  Mosaic  law. 

54.  If  transportation  is  not  felt  as  a severe  punishment,  it 
is  in  itself  ill-suited  to  the  prevention  of  crime  : if  it  is  so  felt, 
much  of  its  severity  is  wasted,  from  its  taking  place  at  too 
great  a distance  to  affect  the  feelings,  or  even  come  to  the 
knowledge,  of  most  of  those  whom  it  is  designed  to  deter  ; but 
one  or  the  other  of  these  must  be  the  case  : therefore  trans- 
portation is  not  calculated  to  answer  the  purpose  of  preventing- 
crime. 

55.  Fontenelle  on  seeing  a criminal  led  to  punishment  said, 
“ There  is  a man  who  has  calculated  badly;  ” whence  it  follows 
that  if  he  could  have  escaped  punishment,  his  conduct  would 
haye  been  laudable. 

56.  If  the  prophecies  of  the  Old  Testament  had  been  writ- 
ten without  knowledge  of  the  events  of  the  time  of  Christ,  they 
could  not  correspond  with  them  exactly ; and  if  they  had  been 
forged  by  Christians,  they  would  not  be  preserved  and  acknow- 
ledged by  the  Jews  : they  are  preserved  and  acknowledged  by 
the  Jews,  and  they  correspond  exactly  with  the  events  of  the 
time  of  Christ ; therefore  they  were  neither  written  without 
knowledge  of  those  events,  nor  were  forged  by  Christians. 

57.  Now  “ if  Christ  be  preached  that  He  rose  from  the 
dead,  how  say  some  among  you  that  there  is  no  resurrection 
from  the  dead  ? But  if  there  be  no  resurrection  of  the  dead 
then  is  Christ  not  risen ; and  if  Christ  is  not  risen  then  is  our 
preaching  vain,  and  your  faith  is  also  vain.  Yea,  and  we  are 
found  false  witnesses  against  God,  because  we  have  testified  of 
God  that  He  raised  up  Christ  whom  he  raised  not  up,  if  so  be 
that  the  dead  rise  not.  For  if  the  dead  rise  not,  then  is  not 
Christ  raised ; and  if  Christ  be  not  raised  your  faith  is  vain, 
ye  are  yet  in  your  sins.  Then  they  also  which  are  fallen 
alseep  in  Christ  are  perished.” 

17 


386 


LOGIC. APPENDIX. 


58.  If  the  bishops  of  England,  before  the  Reformation, 
when  they  were  nominated  by  the  Pope,  were  true  and  valid 
bishops,  then  the  bishops  since  the  Reformation,  when  they 
have  been  nominated  by  the  Crown,  are  not  true  and  valid 
bishops.  But  if  the  bishops  since  the  Reformation,  which 
have  been  nominated  by  the  Crown  are  true  and  valid,  then 
these  before  the  Reformation  are  not  so.  In  either  case  the 
claim  of  Apostolic  succession  and  authority  for  the  English 
bishops  is  absurd. 

§ 4.  Incomplete  and  Compound  Formulae. 

59.  The  study  of  Mathematics  is  essential  to  a complete 
education,  because  it  produces  a habit  of  close  and  constant 
reasoning. 

60.  Familiarity  is  productive  of  contempt,  inasmuch  as  it 
occasions  a needless  exposure  of  private  failings. 

61.  Man  needs  the  restraints  of  law,  since  he  is  naturally 
selfish  ; and  is,  moreover,  subject  to  desires  and  passions  which 
have  no  limits  or  power  of  restraint  in  themselves. 

62.  Sin  is  hateful,  because  it  is  opposed  to  the  Divine  Will. 

63.  A good  face  is  a letter  of  recommendation,  for  it  pre- 
possesses the  beholder  in  favor  of  its  possessor. 

64.  A wise  man  is  never  surprised  because  he  is  never 
disappointed  ; and  he  is  never  disappointed,  because  he  forms 
no  expectations  that  are  not  placed  upon  the  most  certain 
basis. 

65.  Discord  is  a greater  vice  than  intemperance,  since 
discord  always  implicates  more  than  one  person  in  its  guilt. 

66.  Jupiter  was  the  son  of  Saturn ; therefore  the  son  of 
Jupiter  was  the  grandson  of  Saturn. 

67.  They  who  are  not  conscious  of  guilt  are  not  subject  to 
fear  : hence  while  conscious  hypocrites  are  always  shy  and 
timid,  the  innocent  are  unsuspecting  and  self-possessed. 

68.  A negro  is  a man ; whoever,  therefore,  kills  a negro 
wantonly  or  maliciously,  is  guilty  of  murdering  a fellow  man. 

69.  I think ; therefore  I am. 


EXAJMPLES  FOR  CRITICISM. 


387 


70.  Discord  is  not  so  great  an  evil  as  intemperance,  for 
that  generally  arises  from  the  impulse  of  anger  ; while  the  lat- 
ter almost  invariably  proceeds  from  an  uncontrollable  appetite, 
or  an  inveterate  habit. 

71.  Americans  enjoy  a greater  degree  of  political  liberty 
than  any  other  civilized  people,  and  therefore  they  can  have 
no  excuse  for  sedition. 

72.  Hard  substances  are  elastic ; for  ivory  is  both  hard 
and  elastic. 

73.  Meanness  is  never  useful  since  it  is  always  base ; and 
because  it  is  always  honorable  to  be  honest,  it  is  always  useful. 

74.  “ Whosoever  shall  keep  the  whole  law,  and  yet  offend 
in  one  point,  is  guilty  of  the  whole ; for  He  that  said,  Do 
not  commit  adultery,  said  also,  Do  not  kill.” 

75.  The  care  of  the  poor  ought  to  be  the  object  of  all  laws, 
for  the  plain  reason  that  the  rich  can  take  care  of  themselves. 

76.  Wilkes  was  a favorite  with  the  populace  : he  who  is  a 
favorite  with  the  populace  must  understand  how  to  manage 
them  : he  who  understands  how  to  manage  them,  must  be  well 
acquainted  with  their  character  : he  who  is  well  acquainted 
with  their  character,  must  hold  them  in  contempt : therefore 
Wilkes  must  have  held  the  populace  in  contempt. 

77.  The  child  of  Themistocles  governed  his  mother  : she 
governed  her  husband ; he  governed  Athens ; Athens,  Greece ; 
and  Greece,  the  world  : therefore  the  child  of  Themistocles 
governed  the  world. 

78.  The  Scriptures  are  the  standard  of  truth  : and  it  is 
admitted  that  the  Church  of  England  is  in  accordance  with 
the  Scriptures.  Hoadley  was  iu  the  English  Church.  But 
Hoadley  denied  the  divine  institution  of  Episcopacy,  and  the 
authority  of  the  Church  in  matters  of  Faith.  Hence  no  mem- 
ber of  the  English  Church  can  condemn  those  doctrines  as 
unscriptural  or  heretical. 

79.  None  but  whites  are  civilized  : the  Hindoos  are  not 
white ; therefore  the  Hindoos  are  not  civilized. 

80.  None  but  whites  are  civilized  : the  ancient  Germans 
were  whites ; therefore  they  were  civilized.  [See  332-339, 
and  587.] 

- ry. 

Tvo  C j ; L 'pr) 


388 


LOGIC. — APP&rfllX. 

81.  None  but  civilized  people  are  white;  the  Gauls  were 
white,  therefore  they  were  civilized.  [See  587.] 

82.  Popular  commotions,  though  commencing  on  a small 
scale,  are  so  liable  to  ripen  into  systematic  sedition,  that  they 
ought  to  be  speedily  and  decisively  suppressed. 

83.  Every  duty  is  accompanied  with  a certain  propriety 
and  decorum ; whatever,  therefore,  is  not  accompanied  with 
propriety  and  decorum  cannot  be  a duty. 

84.  The  Earth  has  been  repeatedly  circumnavigated ; we 
need,  therefore,  no  other  proof  that  it  is  not  an  interminable 
plane,  as  the  ancients  supposed. 

85.  Whatever  subjects  fall  under  one  and  the  same  general 
definition  are  of  one  and  the  same  kind ; consequently  those 
things  which  do  not  fall  under  that  definition,  must  differ  in 
kind  from  each  other  and  from  all  that  do. 

86.  Those  only  who  understand  other  languages  are  com- 
petent to  teach  correctly  the  principles  of  their  own ; since 
such  a competency  requires  that  philosophic  view  of  language 
which  can  be  acquired  only  by  the  comparison  of  several  with 
each  other. 

87.  Not  a man  of  all  the  antediluvians  escaped  except 
those  that  were  in  the  Ark  with  Noah.  Hence  after  the  flood 
there  were  none  who  had  not  proceeded  from  him  as  their 
progenitor,  and  been  acquainted  with  what  he  knew  of  divine 
things. 

88.  Will  often  combats  desire  as  it  often  also  yields  to  it : 
will  is  not  therefore  desire. 

89.  If  Paley’s  system  is  to  be  received,  one  who  has  no 
knowledge  of  a future  state  has  no  means  of  distinguishing 
virtue  and  vice  : now  one  who  has  no  means  of  distinguishing 
virtue  and  vice  can  commit  no  sin  : therefore,  if  Paley’s  sys- 
tem is  to  be  received,  one  who  has  no  knowledge  of  a future 
state  can  commit  no  sin. 

90.  When  the  observance  of  the  first  day  of  the  week,  as  a 
religious  festival  in  commemoration  of  Christ’s  resurrection, 
was  first  introduced,  it  must  have  been  a novelty  : when  it  was 
a novelty,  it  must  have  attracted  notice:  when  it  attracted 


EXAMPLES  FOE  CEITICISM. 


389 


notice,  it  would  lead  to  inquiry  respecting  the  truth  of  the 
resurrection  : when  it  led  to  this  inquiry,  it  must  have  exposed 
the  story  as  an  imposture,  supposing  it  not  attested  by  living 
witnesses  : therefore  when  the  observance  of  the  first  day  of 
the  week,  &e.  was  first  introduced,  it  must  have  exposed  as  an 
imposture  the  story  of  the  resurrection,  supposing  it  not  at- 
tested by  living  witnesses. 

91.  A system  of  government  which  extends  to  those  ac- 
tions that  are  performed  secretly,  must  be  one  which  refers 
either  to  a regular  Divine  Providence  in  this  life,  or  to  the 
rewards  and  punishments  of  another  world  : every  perfect  sys- 
tem of  government  must  extend  to  those  actions  which  are 
performed  secretly  : no  system  of  government  therefore  can  be 
perfect,  which  does  not  refer  either  to  a regular  Divine  Provi- 
dence in  this  life,  or  to  the  rewards  and  punishments  of  another 
world. 


§ 5.  Miscellaneous  Examples  of  Formulce  and  Fallacies. 

92.  The  end  of  a true  soldier’s  life  is  the  welfare  of  his 
country  : but  death  is  the  end  of  a soldier’s  life  : therefore  his 
death  is  requisite  to  the  safety  and  welfare  of  his  country. 

93.  The  fish  inclosed  in  the  net  were  an  indiscriminate 
mixture  of  all  kinds  : those  that  were  set  aside  and  saved  as 
valuable,  were  fish  that  had  been  inclosed  in  the  net : therefore 
fish  of  all  kinds  were  set  aside  and  saved  as  valuable. 

94.  No  man  can  possess  the  power  to  perform  an  impossi- 
bility. But  a miracle  is  an  impossibility ; therefore  no  man 
can  work  a miracle.  [See  75.] 

95.  Few  scientific  treatises  communicate  truth  in  a clear 
and  conspicuous  manner,  without  any  admixture  of  error. 
Although  a treatise  which  should  so  convey  truth  would  be 
exceedingly  valuable,  yet  it  must  be  admitted  that  there  are 
but  few  treatises  comparatively  which  are  very  valuable. 

96.  All  the  miracles  of  Jesus  would  fill  more  books  than 
the  world  could  contain ; the  things  related  by  the  Evangel- 
ists are  the  miracles  of  Jesus  : therefore  the  things  related  by 
the  Evangelists  would  fill  more  books  than  the  world  could 
contain. 


390 


LOGIC. APPENDIX. 


97.  If  a man  say,  I love  God,  and  hateth  liis  brother,  he 
is  a liar ; for  he  that  loveth  not  his  brother,  whom  he  hath 
seen,  how  can  he  love  God  whom  he  hath  not  seen  ? 

98.  If  the  Romish  doctrine  of  Transubstantiation  be  true, 
in  receiving  the  Eucharist,  the  Romanists  are  guilty  of  can- 
nibalism. But  if  they  are  not  guilty  of  cannibalism  their 
doctrine  is  false.  [See  221.] 

99.  The  principles  of  justice  are  variable ; the  appoint- 
ments of  nature  are  invariable  : therefore  the  principles  of 
justice  are  no  appointment  of  nature. 

100.  A story  is.  not  to  be  believed,  the  reporters  of  which 
give  contradictory  accounts  of  it ; the  story  of  the  life  and 
exploits  of  Bonaparte  is  of  this  description  : therefore  it  is  not 
to  be  believed. 

101.  It  is  certain  that  in  the  moral  government  of  God, 
virtue  will  produce  happiness  and  vice  will  produce  misery. 
We  may  therefore  say,  that  whatever  will  produce  happiness 
is  virtue,  and  define  virtue  to  be  the  pursuit  of  happiness  in 
accordance  with  the  will  of  God. 

102.  It  is  evident  that  drunkenness  is  a sin  most  odious 
in  the  sight  of  God.  It  is  equally  certain  that  the  use  of 
alcohol  is  destructive  to  the  moral  and  physical  energies  of 
man.  I claim,  therefore,  not  only  that  it  is  the  duty  of  every 
man  to  abstain  totally  from  the  use  of  alcoholic  drinks,  but 
as  a good  citizen  and  a philanthropist,  to  exert  all  his  influence 
to  obtain  and  enforce  a law  which  shall  totally  prevent  the 
sale  of  intoxicating  drinks  of  any  kind. 

103.  Nothing  which  is  of  less  frequent  occurrence  than  the 
falsity  of  testimony  can  be  fairly  established  by  testimony  ; 
any  extraordinary  and  unusual  fact  is  a thing  of  less  frequent 
occurrence  than  the  falsity  of  testimony  (that  being  very  com- 
mon) : therefore  no  extraordinary  and  unusual  fact  can  be 
fairly  established  by  testimony. 

104.  Testimony  is  a kind  of  evidence  which  is  very  likely 
to  be  false ; the  evidence  on  which  most  men  believe  that 
there  are  pyramids  in  Egypt  is  testimony  : therefore  the  evi- 
dence on  which  most  men  believe  that  there  are  pyramids  in 
Egypt  is  very  likely  to  be  false. 


EXAMPLES  FOE  CKITICISH. 


391 


105.  He  who  cannot  possibly  act  otherwise  than  he  does, 
has  neither  merit  nor  demerit  in  his  action.  A liberal  and 
benevolent  man  in  relieving  the  sufferings  of  the  poor  cannot 
do  otherwise  than  relieve  them : therefore  there  is  no  merit  in 
his  actions. 

106.  Slavery  is  an  outrage  upon  the  inalienable  rights 
of  man.  It  operates,  wherever  it  exists,  as  a means  of  corrup- 
tion and  degeneracy  to  the  social  and  political  condition  of 
mankind.  Hence,  as  citizens,  as  Christians,  and  as  philanthro- 
pists, we  are  called  upon  to  labor  for  the  promotion  of  its  im- 
mediate abolition. 

107.  It  is  generally  held  that  St.  Paul  wrote  the  Epistle 
to  the  Romans.  But  th^  Epistle  itself  expressly  declares  that 
Tertius  wrote  it  (xvi.  22).  Therefore  St.  Paul  cannot  pro- 
perly be  regarded  as  its  author. 

108.  The  publication  of  a libel  is  criminal : but  the  act 
of  putting  a libel  into  the  post,  is  an  act  of  publication  (for  the 
moment  a man  passes  the  libel  from  his  hand  his  control  over 
it  is  gone) ; that  act,  therefore,  must  be  pronounced  criminal. 

109.  True  wisdom  cannot  be  too  dearly  purchased.  Hu- 
mility always ' accompanies  true  wisdom  : therefore  humility 
cannot  be  too  dearly  purchased. 

110.  No  man  could  bind  him,  no  not  with  chains;  because 
that  he  had  been  often  bound  with  fetters  and  chains,  and  the 
chains  had  been  broken  asunder  by  him,  and  the  fetters  broken 
in  pieces.  [See  425.] 

111.  That  which  is  greater  than  faith  and  hope  must  be 
the  highest  Christian  grace.  Charity,  therefore,  which  is  but 
another  name  for  almsgiving,  is  greater  than  faith  and  hope, 
and  must  therefore  be  more  important  than  any  degree  of 
accuracy  or  orthodoxy  in  the  faith. 

112.  It  is  sufficient  to  show  the  fallacy  of  the  Protestant 
dogma,  ‘‘  the  Bible,  and  the  Bible  alone  is  the  religion  of  the 
Protestants,”  to  state  the  fact,  that  many  parts  of  the  Bible 
are  wanting,  as  for  example,  the  Book  of  the  Wars  of  the 
Lord,  the  Book  of  Jasher,  and  of  the  New  Testament,  the 
Epistle  to  the  Laodiceans,  to  mention  no  more.  If,  therefore, 
the  whole  Bible  would  be  a sufficient  rule  of  faith  to  the 


392 


LOGIC. APPENDIX. 


Protestant  if  lie  possessed  it,  yet  since  lie  has  not  the  'whole, 
what  he  has  can  be  no  sufficient  rule. 

113.  The  New  Testament  as  a distinct  book,  was  nevei 
heard  of  until  the  Council  of  Laodicea,  which  at  the  earliest  was 
314  years  after  the  commencement  of  the  Christian  era.  It  is, 
threfore,  absurd  to  pretend  that  it  was  written  by  the  Apos- 
tles, who  were  all  dead  more  than  a century  before  this  date. 

114.  A collection  of  rules,  designed  to  enable  us  to  under- 
stand the  principles  of  any  subject,  is  a science  ; but  if  those 
rules  are  designed  to  assist  us  in  the  application  of  these  prin- 
ciples to  a specific  end,  they  constitm/e  an  art.  Now  Logie 
collects  and  states  the  rules  with  a view  to  the  comprehension 
of  the  rules  themselves  ; but  Rhetoric*with  a view  to  their  ap- 
plication to  the  specific  end  of  conviction  and  persuasion  : 
therefore  Logic  is  a science,  and  Rhetoric  is  an  art. 

115.  Russia  knows  full  well  that  she  is  engaged  in  a con- 
test with  two  nations  that  were  never  yet  overcome  by  valor 
of  arms,  nor  circumvented  by  fraud  or  cunning  in  diplomacy. 
Rut  Russia  is  contending  against  France  and  England : there- 
fore neither  France  nor  England  was  ever  overcome  by  valor, 
or  circumvented  by  cunning  or  fraud. 

116.  If  the  forgiveness  of  sins  was  imparted  at  one’s  con- 
version, Ananias  could  not  have  said  to  St.  Paul  three  days 
after  his  conversion,  “ Arise,  be  baptised,  and  wash  away  thy 
sins.”  But  such  was  precisely  the  message  which  he  was 
commissioned  by  the  Holy  Ghost  to  deliver  to  him ; therefore 
remission  of  sins  takes  place  in  Baptism. 

117.  An  unholy  minister  is  the  greatest  of  all  sinners; 
for  either  he  is  a person  of  more  than  ordinary  knowledge  or 
he  is  not.  If  he  is  not,  he  sinned  greatly  in  undertaking  that 
office,  for  which  so  great  knowledge  is  required.  If  he  be,  his 
knowledge  will  doubtless  increase  his  guilt. 

118.  - The  works  of  creation  imply  far  more  of  design  and 
of  wisdom  than  the  Iliad  of  Homer  or  the  Geometry  of  Euclid. 
But  no  one  ever  supposed  that  the  Iliad,  or  the  Geometry  of 
Euclid  were  composed  without  an  intelligent  author ; there- 
fore the  works  of  creation  must  have  had  an  Intelligent 
Creator. 

119.  The  Jesuit  cites  Ruffinus  in  proof  of  the  infallibility 


EXAMPLES  FOK  CRITICISM. 


393 


of  his  church.  But  if  Ruffinus  is  right  the  church  is  not  in- 
fallible, since  it  does  not  agree  with  Ruffinus.  If,  however, 
Ruffinus  is  wrong,  his  testimony  is  worthless. 

120.  The  doctrine  which  holds  to  an  omnipresent  divine 
power  and  agency  in  the  operations  of  Nature,  is  as  contrary 
to  the  Scriptures  as  it  is  to  sound  philosophy ; for  the  Scrip- 
tures say  expressly,  “ the  earth  bringeth  forth  fruit  of  herself  ” 
(St.  Mark  iv  28). 

121.  Nature  is  either  the  author  of  Nature,  or  it  is  the 
order  of  things  established  by  a Supreme  Intelligence.  But 
nothing  can  be  the  author  of  itself;  therefore,  Nature  can  be 
only  the  order  of  things  established  by  a Supreme  Intelli- 
gence. 

•122.  The  cause  of  evil  is  itself  an  evil.  But  that  Chris- 
tianity has  caused  much  evil  in  the  shape  of  wars,  oppression, 
imposture,  fanaticism,  and  persecution,  cannot  be  denied. 

123.  Our  Lord  said,  “ If  a man  keep  my  saying  he  shall 
never  taste  of  death.  Then  said  the  Jews  unto  Him,  Now  we 
know  that  thou  hast  a devil.  Abraham  is  dead,  and  the  Pro- 
phets. Art  thou  greater  than  our  father  Abraham  ? whom 
makest  thou  thyself  ? ” 

124.  “ The  argument  of  the  atheist  assumes  that  it  is  pos- 
sible to  create  an  intelligent  moral  agent,  and  place  it  beyond 
all  liability  to  sin.  But  this  is  a mistake.  Almighty  Power 
itself  cannot  create  such  a being,  and  place  it  beyond  the  pos- 
sibility of  sinning,  as  we  shall  prove,”  &c. 

125.  He  who  has  a confirmed  habit  of  any  kind  of  action, 
exercises  no  self-denial  in  the  practice  of  that  action  ; a good 
man  has  a confirmed  habit  of  virtue ; therefore  he  who  exer- 
cises self-denial  in  the  practice  of  virtue  is  not  a good  man. 

126.  He  is  the  greatest  lover  of  any  one  who  seeks  that 
person’s  greatest  good ; a virtuous  man  seeks  the  greatest 
good  for  himself ; therefore  a virtuous  man  is  the  greatest 
lover  of  himself. 

127.  Whatever  is  real  is  limited  [by  that  which  it  is  not]. 
But  whatever  is  limited  is  not  infinite ; therefore  if  God  is 
real,  and  not  a mere  fiction  of  the  imagination,  He  is  not  an 
infinite  being. 


17* 


391 


LOGIC. — APPENDIX. 


128.  Theft  is  a crime  : theft  was  encouraged  by  the  laws 
of  Sparta  ; therefore  the  laws  of  Sparta  encouraged  crime. 

129.  Every  hen  comes  from  an  egg  : every  egg  comes  from 
a hen  : therefore  every  egg  comes  from  an  egg. 

130.  Nothing  is  heavier  than  platina  : feathers  are  heavier 
than  nothing  : therefore  feathers  are  heavier  than  platina. 

131.  Meat  and  drink  are  necessaries  of  life  : the  revenues 
of  Yitellius  were  spent  on  meat  and  drink ; therefore  the 
revenues  of  Yitellius  were  spent  on  the  necessaries  of  life. 

132.  No  evil  should  be  allowed  that  good  may  come  of  it. 
But  all  punishment  is  an  evil ; therefore  no  punishment  should 
be  allowed. 

133.  Repentance  is  a good  thing.  But  no  persons  have 
so  much  repentance  as  the  wicked ; therefore  none  have  so 
much  good  as  the  wicked. 

134.  He  who  bears  arms  at  the  command  of  the  magis- 
trate does  what  is  lawful  for  a Christian.  The  Swiss  in  the 
French  service,  and  the  British  in  the  American  service  bore 
arms  at  the  command  of  the  magistrate ; therefore  they  were 
doing  only  what  was  lawful  for  a Christian  to  do. 

135.  He  who  calls  you  a man  speaks  the  truth ; but  he 
that  calls  you  a knave  calls  you  a man ; therefore  he  who  calls 
you  a knave  speaks  the  truth. 

[This  Minor  Premise  may  be  pronounced  a non  vera.  But  I should 
prefer  to  refer  the  Formula  to  the  Fallacy  of  Accidents  (750,  1057-8). 
In  this  view  we  must  regard  as  accidental,  that  which  is  not  in  the  Con- 
ception when  used  as  a Predicate  (195),  however  essential  it  may  be  to 
the  existence  of  any  individual  in  that  genus  among  the  realities  of 
being.] 

136.  A monopoly  of  the  sugar-refining  business  is  bene- 
ficial to  sugar-refiners  ; and  of  the  corn-trade  to  corn-growers ; 
and  of  the  silk-manufacture  to  silk-weavers,  &c.,  &c. ; and 
thus  each  class  of  men  are  benefited  by  some  restrictions. 
Now  all  these  classes  of  men  make  up  the  whole  community ; 
therefore  a system  of  restrictions  is  beneficial  to  the  community. 
[See  58-60,  748.] 

137.  “We  have  seen  in  a preceding  chapter,  that  naturally 
no  man  has  any  authority  over  another — his  pursuits,  his  posses- 
sions, his  life  or  his  liberty,  except  what  arises  from  the  pri- 


EXAMPLES  FOE  CRITICISM. 


395 


mary  law  of  nature,  self-defence.  Now  as  a State  is  made  up 
of  men,  the  State  can  have  no  authority  which  each  man  in  the 
State  did  not  possess  before  he  entered  into  the  body  politic. 
And  from  this  it  follows,  not  only  that  capital  punishment, 
banishment,  and  such  like  punishments  are  unauthorized  and 
wrong,  but  that  all  attempts  on  the  part  of  the  State  to  pro- 
mote education,  impose  oaths,  or  to  encourage  religion  in  any 
form,  or  to  regulate  the  institution  of  marriage  in  any  way, 
is  a tyrannical  assumption  of  rights  over  man,  which  power 
may  indeed  enable  it  to  enforce,”  &c.,  but  nothing  can  jus- 
tify. [58.] 

138.  If  the  diiference  in  the  various  races  of  men  has  not 
been  produced  by  climatic  causes,  they  must  each  of  them  have 
had  a separate  proto-plastic  pair  for  their  progenitors.  But 
these  differences  cannot  have  been  produced  by  climatic  causes  ; 
therefore  the  races  cannot  have  sprung  from  the  same  parents 
originally.  [See  400  and  412.] 

139.  Opium  is  a poison ; but  physicians  advise  some  of 
their  patients  to  take  Opium ; therefore  physicians  advise 
some  of  their  patients  to  take  poison. 

140.  Animal  food  may  be  entirely  dispensed  with  (as  is 
shown  by  the  practice  of  the  Brahmins  and  of  some  monks) : 
and  vegetable  food  may  be  entirely  dispensed  with  (as  is  plain 
from  the  example  of  the  Esquimaux  and  others)  : but  all  food 
consists  of  animal  food  and  vegetable- food  ; therefore  all  food 
may  be  dispensed  with. 

141.  I have  shown,  gentlemen,  that  it  is  the  natural  right 
of  all  God’s  creatures  to  be  free.  I have  shown  that  a 
people  having  the  same  tongue,  historic  recollections  and 
associations,  conveniently  situated,  and  existing  in  sufficient 
numbers  for  the  purpose,  are  entitled  to  a distinct  national 
existence ; and  I claim,  therefore,  not  only  the  sympathy  of 
Americans  for  my  poor  and  oppressed  Hungary,  which  I know 
that  I shall  have,  but  also  their  intervention  as  a nation,  and 
their  generous  liberality  in  furnishing  the  material  aid  neces- 
sary to  enable  us  to  carry  on  our  struggle,  and  secure  our 
independence  of  Austrian  rule  and  despotism. 

142.  Whilst  all  other  sorts  and  orders  of  men  conversed 
with  our  Lord,  never  do  we  hear  of  any  interview  between 
Him  and  the  Essenes.  Suppose  one  Evangelist  to  have 


396- 


LOGIC. APPENDIX. 


overlooked  such  a scene,  another  would  not.  One  Evangelist 
was  impressed  with  one  scene  and  a second  by  another.  And 
thus  it  must  have  happened  that,  amongst  the  four,  at  least 
one  would  have  noticed  the  Essenes.  But  no  one  of  the  four 
Gospels  alludes  to  them.  The  Acts  of  the  Apostles  is  a fifth 
body  of  recollections,  but  this  does  not  notice  them.  The  Apo- 
calypse of  St.  John  says  not  one  word  about  them.  St.  Peter 
and  St.  James  in  their  Epistles  entirely  overlook  them.  St. 
Paul  gives  no  sign  that  he  had  ever  heard  of  them.  Where- 
fore we  must  conclude  that  there  was  no  sect  known  by  that 
name,  except  iu  the  delusions  conjured  up  by  his  own  igno- 
rant heart  (Josephus). 


§ 6.  Examples  presenting  Questions  of  Method. 

143.  All  the  facts  of  man’s  mental  activity  may  be  referred 
to  two  classes,  Spontaneity  and  Beflection.  But  of  the  two 
classes,  the  spontaneous  must  be  first  in  point  of  time.  For 
reflection  implies  volition,  and  volition  implies  that  the  thing 
chosen  is  already  in  the  mind,  as  an  object  of  conscious 
thought  before  the  choice.  Hence  it  could  not  have  been  given 
in  reflection,  and  must  therefore  have  been  given  in  spon- 
taneity. 

144.  “ With  God  nothing  is  impossible.”  But  God  can- 
not make  the  three  angles  of  a triangle  more  than  two  right 
angles  ; therefore  some  things  are  impossible  with  God.  [See 
4:23,  424.] 

145.  The  religion  of  the  ancient  Greeks  and  Romans  was 
a tissue  of  extravagant  fables  and  groundless  superstitions, 
credited  by  the  vulgar  and  the  weak,  and  maintained  by  the 
more  enlightened,  from  selfish  or  political  views  : the  same 
was  clearly  the  case  with  the  religion  of  the  Egyptians  : the 
same  may  be  said  of  the  Brahminical  worship  of  India,  and 
the  religion  of  Fo  professed  by  the  Chinese  : the  same  of  the 
romantic  mythological  system  of  the  Peruvians,  of  the  stern 
and  bloody  rites  of  the  Mexicans,  and  those  of  the  Britons  and 
of  the  Saxons  : hence  we  may  conclude  that  all  systems  of 
religion,  however  varied  iu  circumstances,  agree  in  being  super- 
stitions kept  up  among  the  vulgar,  from  interested  or  political 
views  in  the  more  enlightened  classes. 


EXAMPLES  FOE  CEITICISM. 


39T 


146.  A feeble  Executive  implies  a feeble  execution  of  the 
Government.  A feeble  execution  is  but  another  name  for  a 
bad  execution ; and  a government  ill  executed,  whatever  it 
may  be  in  theory  must  be  in  practice  a bad  government. 
Hence  with  a feeble  or  inefficient  executive,  a government 
will  always  be  bad,  whatever  may  be  its  form  or  its  theory. 

147.  In  the  Scriptures  it  is  written  concerning  the  Church, 
and  we  see  that  the  Church  exists.  There  it  is  written  con- 
cerning idols  that  they  shall  cease,  and  we  see  that  they  are 
not.  There  it  is  written  that  the  Jews  were  to  lose  the  king- 
dom, and  we  see  that  the  fact  is  so.  There  it  is  written  con- 
cerning heretics  that  they  should  exist,  and  we  see  that  it  is  so. 
There  it  is  written  also  concerning  the  Day  of  Judgment.  There 
it  is  written  concerning  the  rewards  of  the  good  and  the  punish- 
ment of  the  wicked.  In  all  things  we  have  found  God  faith- 
ful. Will  He  fail  and  deceive  us  in  the  last  ? 

148.  I maintain  that  the  Fugitive  Slave  Law  is  uncon- 
stitutional, or  at  least  a law  not  required  by  the  Constitution. 
“ Slaves  ” are  not  mentioned  in  the  clause  requiring  the  ren- 
dition of  persons  held  to  service  in  one  State  escaping  into 
another.  The  gentlemen  [of  the  South]  say  indeed  that  slaves 
are  included  in  the  scope  and  intent  of  the  law.  But  I answer 
so  are  undoubtedly  the  Negroes,  who  have  been  admitted  to 
citizenship  in  the  Northern  States,  included  in  that  clause  of 
the  Constitution  which  declares  that  the  “ citizens  of  each 
State  are  entitled  to  the  privileges  and  immunities  of  citizens 
in  any  of  the  other  States  into  which  they  may  go  to  reside.” 
And  they  exclude  Negro  citizens  of  the  Northern  States  from 
citizenship  in  their  States,  if  they  choose  to  go  into  their 
borders. 

149.  St.  Paul  says,  “ Whom  God  did  foreknow  He  also  did 
predestinate  to  be  conformed  to  the  image  of  his  Son.  More- 
over whom  He  did  predestinate  them  He  also  called,  and  whom 
He  called  them  He  also  justified,  and  whom  he  justified  He 
also  glorified.”  But  Christians,  so  long  as  they  are  living  in 
the  body  are  not  glorified  ; therefore  they  are  not  among  those 
of  whom  St.  Paul  was  speaking  as  predestinated  by  God  to  be 
conformed  to  the  image  of  His  Son. 

150.  If  these  acts  are  valid,  the  old  corporation  is  abol- 
ished and  a new  one  created.  The  first  act  does,  in  fact,  if  it 


398 


LOGIC. APPENDIX. 


can  have  any  effect,  create  a new  corporation , and  transfer  to  it 
all  the  property  and  franchises  of  the  old.  The  two  corpora- 
tions are  not  the  same  in  any  thing  which  essentially  belongs 
to  the  existence  of  a corporation.  They  have  different  names 
and  different  powers,  rights  and  duties.  Their  organization  is 
wholly  different.  The  powers  of  the  corporation  are  not  vested 
in  the  same  or  similar  hands ; and  the  act  itself  provides  for 
the  first  meeting  and  organization  of  the  new  corporation.  It 
expressly  provides  that  the  new  corporation  shall  have  and 
hold  all  the  property  of  the  old ; a provision  which  would  be 
cjuite  unnecessary  upon  any  other  ground  than  that  the  old 
corporation  was  dissolved. 

151.  It  has  been  noticed  that  when  we  see  a good  act  per- 
formed, we  approve  the  act  and  feel  a sympathy  with  the  agent. 
It  has  hence  been  laid  down  as  a fundamental  principle  in 
Ethics,  that  those  actions  are  good  which  thus  elicit  our  sym- 
pathy and  approbation.  But  this  is  a false  criterion.  It  implies 
a judgfnenit  concerning  the  act,  “ it  is  good,”  and  a feeling  or 
emotion,  and  holds  that  the  judgment  is  based  upon  the  emo- 
tion. But  the  judgment  precedes  and  is  the  cause  of  the 
emotion,  for  the  emotion  will  always  remain  the  same  so  long 
as  our  estimate  of  the  act  remains  unchanged.  But  let  us 
hear  something  concerning  the  act  which  changes  our  estimate 
of  its  character,  and  the  emotion  or  feeling  towards  the  person 
who  performed  it  changes  also. 

152.  If  a paste  be  made  of  wheat  flour,  boiled  in  water, 
and  allowed  to  stand  for  a few  days,  there  will  be  in  it  not 
only  small  plants  or  vegetables,  but  also  small  animalculse. 
Now  the  boiling  would  of  itself  have  destroyed  all  the  seeds 
of  vegetables,  as  well  as  the  ova  of  any  animal  existence,  so 
that  we  are  led  inevitably  to  the  conclusion  that  inorganic 
matter  will  produce  both  vegetable  and  animal  life,  without 
the  seeds  or  ova  ofi^  preceding  plants  or  animals  of  the  same 
species ; and  if  so,  the  theory  of  creation,  and  a personal 
Creator,  is  shown  to  be  unnecessary  to  philosophy,  and  even 
unphilosophical. 

153.  It  is  said  that  at  death  all  appearance  of  life  becomes 
extinct,  and  every  indication  of  a total  cessation  of  existence 
is  presented. 

But  in  the  first  place  we  see  that  parts  of  the  body,  as 


EXAMPLES  FOE  CRITICISM. 


399 


hands,  feet,  &c.,  may  die  and  decay,  and  the  soul  remain  en- 
tirely unimpaired. 

Again,  it  is  a principle  which  prevails  every  where  in 
Nature,  that  nothing  once  in  existence  can  be  lost.  The  wood 
that  is  consumed  in  the  fire  is  resolved  thereby  into  its  ele- 
ments, but  every  particle  of  it  exists  somewhere.  So  with  the 
body  at  death.  But  the  soul  being  immaterial  is  not  capable 
of  dissolution,  or  resolution  into  constituent  elements. 

Again,  we  have  frequent  cases  of  change  of  the  form  of 
existence,  without  a cessation  of  the  existence  of  that  whose 
form  is  changed.  Such  changes  we  have  in  the  foetus  in 
passing  from  its  state  before  birth  to  its  mode  of  life  after ; in 
the  chick  emerging  from  the  shell,  and  especially  in  the  case 
of  all  the  metabolians  which  appear  as  worms  : these  go  into  a 
state  of  apparent  death,  and  after  a while  emerge  as  insects 
with  wings. 

In  all  these  cases  that  which  is  once  in  being,  continues 
to  exist  notwithstanding  the  changes  in  its  form  or  state  of 
existence.  Hence  we  may  conclude  that  the  human  soul  will 
do  so  likewise  at  death. 

154.  Some  years  since  there  appeared  in  the  West  a dis- 
ease, which  was  called  the  milk- sickness.  The  following  hypo- 
theses were  suggested  as  accounting  for  it;  namely,  that  (1)  it 
proceeded  from  some  miasma  in  the  air  ; (2)  from  some  pecu- 
liarity in  the  ivaier  ; (3)  from  arsenic,  cobalt,  and  other  mine- 
rals in  the  soil;  and  finally,  (4)  that  it  was  owing  to  some 
disease  in  the  vegetable  productions. 

As  facts  it  was  found  : (1)  that  its  appearance  was  con- 
fined within  narrow  limits ; (2)  that  when  it  makes  its  appear- 
ance among  men,  there  has  heen  preceding  it  a disease  among 
the  animals,  ealled  the  Slows  or  Trembles.  It  is  also  ascer- 
tained (3)  that  the  flesh,  the  milk,  the  butter,  and  the  cheese 
made  from  animals  having  the  Slows,  causes  the  milk-sickness 
in  men  [hence  its  name]  ; (4)  the  disease  appears  in  pastures 
where  there  is  no  water  ; and  (5)  the  flesh  of  animals  diseased 
imparts  none  of  its  poisonous  properties  to  the  water  in  which 
it  is  boiled ; (6)  the  disease  affects  those  animals  which  graze 
at  night,  and  especially  in  the  woods  ; (7)  carnivorous  animals 
never  have  the  disease  until  they  have  taken  it  by  eating  ani- 
mals already  affected  ; and  (8)  females  during  lactation,  cows, 
sluts,  &c.,  often  escape  the  disease  themselves  after  having 


400 


LOGIC. APPENDIX. 


eaten  the  poison,  but  communicate  it  to  their  offspring.  And 
(9)  in  those  cases  in  which  the  flesh  of  diseased  animals  had 
been  swallowed  aud  vomited  up  soon  afterwards,  there  was 
either  no  disease  or  only  very  little  following.  [To  be  treated 
as  a case  of  Elimination.] 

155.  The  various  systems  of  pagan  idolatry  correspond  so 
closely,  that  they  cannot  have  been  struck  out  independently 
in  the  several  countries  where  they  have  been  established,  and 
must  therefore  have  originated  from  a common  source.  But 
if  they  had  a common  source,  then  either  one  nation  must  have 
communicated  its  peculiar  theology  to  every  other  people  in 
the  way  of  peaceful  and  voluntary  imitation,  or  through  the 
medium  of  conquest  and  violence ; or  all  nations  must  have 
been  assembled  together  in  a single  community,  and  then  agreed 
to  adopt  the  theology  in  question  as  a new  and  recent  inven- 
tion ; or,  having  received  it  from  the  past,  and  believing  it  on 
whatever  grounds  to  be  true,  they  must  have  carried  it  with 
them  as  from  that  common  centre  to  all  parts  of  the  globe. 
The  first  and  second  are  impossible  in  the  nature  of  things ; 
therefore  all  these  various  systems  must  have  had  a common 
origin. 

But  the  third  position  is  nearly  as  incredible  as  either  the 
first  or  the  second  ; namely,  that  they  should  have  all  agreed 
in  one  stupendous  system  of  imposture,  professing  to  believe 
as  divine  that  which  they  knew  that  they  had  of  themselves 
but  recently  invented. 

Idolatry,  therefore,  must  have  arisen  before  the  dispersion 
of  mankind,  and  be  a corruption  of  a tradition  that  was  be- 
lieved true  at  au  age  St)  near  to  the  origin  of  the  race  (or  its 
restoration  after  the  flood),  that  its  foundation  must  have  been 
in  the  truths  which  were  either  observed  by  man,  or  super- 
naturally  communicated  to  him  at  the  time  of  his  creation. 

156.  The  fundamental  doctrines  and  institutions  of  Chris- 
tianity are  not  to  be  held  as  mere  opinions,  with  regard  to 
which  men  may  innocently  differ,  and  be  entitled  in  their  diver- 
sities to  that  consideration  and  respect  to  which  they  are  enti- 
tled in  matters  of  mere  indifference  or  uncertainty.  For  other- 
wise no  persons  could  be  allowed  to  affirm  the  truth  with  that 
confidence  and  certainty  which  its  proper  influence  requires. 
It  follows,  moreover,  from  the  wisdom  and  justice  of  God,  that 
the  evidence  of  the  truth  of  those  doctrines  and  institutions  is 


EXAMPLES  FOR  CRITICISM. 


401 


such  that  they  cannot  he  innocently  rejected.  If  God  is  infi- 
nitely wise  he  knew  what  was  sufficient  evidence,  and  if  He  is 
just  He  would  never  require  belief  and  obedience  without  giv- 
ing such  evidence  as  would  throw  the  guilt  of  unbelief  upon 
the  unbeliever.  And  in  all  other  cases,  in  all  departments  of 
thought,  we  hold  to  certain  fundamental  principles  with  regard 
to  which  we  allow  of  no  differences  of  opinion,  which  we  ac- 
knowledge to  be  entitled  to  respect.  In  Geometry,  in  Astro- 
nomy, in  Mechanics,  every  where  in  fact,  we  expect  the  assent 
of  all  intelligent  and  well-disposed  men  to  certain  fundamental 
principles.  We  do  not  treat  the  man  who  pretends  to  science, 
and  yet  denies  that  the  earth  revolves  on  its  axis  around  the 
sun,  instead  of  the  sun’s  moving  around  the  earth  as  entitled 
to  argument.  We  regard  him  as  either  a fool  or  a madman. 
In  like  manner  the  Articles  of  Faith  contained  in  the  Apos- 
tles’ Creed,  the  Ministry,  the  Worship,  and  the  Sacraments  of 
the  Church,  have  been  held  in  all  ages  of  the  Church  as  too 
fundamental  in  their  character,  and  too  fully  and  obviously 
revealed  in  the  Scriptures,  to  be  properly  regarded  as  mere 
subjects  of  opinion  and  preference,  in  regard  to  which  unbelief 
could  be  innocent  or  properlv  entitled  to  favor. 


§ 7.  Abstract  of  Leslie’s  Short  and  Easy  Method. 

“ What  you  ask  and  I undertake  to  accomplish,  is  to  furnish 
some  one  topic  of  reason  which  shall  demonstrate  the  truth  of 
the  Christian  Religion,  and  at  the  same  time  distinguish  it 
from  the  impostures  of  Mahomet  and  whole  pagan  world.” 

“ If  the  matters  of  fact  which  are  recorded  in  the  Gospels 
be  true,  the  truth  of  doctrine  of  Christ  will  be  sufficiently 
evinced  ; for  if  His  miracles  be  true  they  do  vouch  the  truth 
of  what  He  delivered.” 

“ The  same  is  to  be  said  as  to  Moses  and  the  Old  Testa- 
ment.” 

I shall  then  first  lay  down  such  rules  as  to  the  truth  of 
matters  of  fact  in  general,  that  where  they  all  meet,  such  mat- 
ters of  fact  cannot  be  false.  And  then,  secondly , I shall  show 
that  all  these  rules  do  meet  in  the  matters  of  fact  of  Moses  and 
of  Christ ; and  that  they  do  not  meet  in  the  matters  of  fact  of 
Mahomet  and  the  Heathen  deities,  nor  can  possibly  meet  in  any 
imposture  whatever. 


402 


LOGIC. APPENDIX. 


I.  The  Rules  are  : 

1st.  That  the  matters  of  fact  be  such  as  that  men’s  out- 
ward senses,  their  eyes  and  ears  may  be  judges  of  it. 

2d.  That  it  be  done  publicly  in  the  face  of  the  world. 

3d.  That  not  only  public  monuments  be  kept  up  in  memory 
of  it,  but  some  outward  actions  to  be  performed. 

4th.  That  such  monuments,  and  such  actions  or  observ- 
ances be  instituted,  and  do  commence  from  the  time  that  the 
matter  of  fact  was  done. 

The  two  first  rules  make  it  impossible  for  any  such  matter 
of  fact  to  be  imposed  upon  men  at  the  time  when  such  matter 
of  fact  was  said  to  be  done. 

The  only  alternative,  therefore,  is  that  such  matter  of  fact 
might  be  invented  some  time  after. 

But  against  this  the  two  last  rules  (3d  and  4th)  secure  us, 
as  much  as  the  two  first  rules  in  the  former  case. 

II.  The  matters  of  fact  of  Moses  and  of  Christ  have  all 
these  rules  or  marks  before  mentioned,  and  that  neither  the 
matters  of  fact  of  Mahomet,  nor  what  is  reported  of  the  Hea- 
then deities  have  the  like,  and  that  no  imposture  can  have 
them  all. 

As  to  Moses.  He  persuaded  the  Israelites  that  he  had 
brought  600,000  of  them  from  Egypt  and  through  the  Red 
Sea,  that  he  fed  them  forty  years  without  bread  by  a miracu- 
lous manna.  But  he  could  not  have  persuaded  them  of  these 
facts  if  they  had  not  been  true,  since  every  man’s  senses  that 
were  then  alive  must  have  contradicted  it.  So  that  here  are 
th q first  and  second  of  the  above-mentioned  four  marks. 

For  the  same  reason  it  would  have  been  impossible  for 
him  to  persuade  them  to  receive  his  five  Books  (the  Penta- 
teuch) as  truth,  unless  they  were  so ; since  in  those  books  he 
constantly  appeals  to  them  as  eye  and  ear  witnesses  of  those 
things. 

The  utmost  that  we  can  suppose  then  is,  that  these  Books 
were  written  in  some  age  after  Moses  and  put  out  in  his  name. 

But  in  that  case  it  is  impossible  that  the  Books  should 
have  been  received,  for  they  speak  of  themselves  as  delivered 
by  Moses,  and  kept  in  the  Ark  from  his  time,  and  likewise  a 
copy  with  the  King. 

Now  in  whatever  age  we  may  suppose  the  imposture  to 
have  been  attempted,  it  was  impossible  that  it  should  be 


EXAMPLES  FOE  CEITICISM. 


403 


received  as  truth,  since  no  such  copy  would  have  been  in  ex- 
istence in  the  Ark  or  in  the  King’s  possession,  as  the  Book 
itself  claims. 

But  besides  this  the  Book  speaks  of  laws  and  ordinances, 
and  of  the  time  and  circumstances  of  their  origin,  and  claims 
that  they  had  been  observed  from  the  time  of  their  origin,  as 
of  the  Passover,  the  institution  of  the  Levites,  the  budding  of 
Aaron’s  rod,  which  was  still  kept  in  the  Ark,  the  pot  of  manna, 
the  brazen  serpent,  and  the  Feast  of  Pentecost.  Then  there 
was  also  the  Sabbath,  the  daily  sacrifices,  the  yearly  expiation, 
the  new  moons,  and  other  monthly,  weekly,  and  daily  remem- 
brances and  recognitions  of  these  things.  Here  then  the  third 
and  fourth  marks  mentioned  above  are  found. 

But  suppose  that  these  things  had  been  practised  before 
the  Books  of  Moses  were  forged ; that  these  Books  imposed 
upon  the  people  only  in  making  them  believe  that  they  had 
kept  these  observances  in  memory  of  what  had  never  occurred. 

Now  this  supposes  that  the  Jews  kept  these  observances 
either  in  memory  of  nothing,  or  without  knowing  what  they 
commemorated. 

But  the  observances  themselves  express  the  ground  and 
reason  of  their  being  kept. 

Again,  suppose  the  Jews  did  not  know  any  reason  why 
they  kept  these  observances,  and  that  they  were  persuaded 
that  they  had  been  keeping  them  as  observances  of  that  of 
which  they  had  never  heard  before. 

Does  any  Deist  think  it  possible  that  such  a cheat  could  pass  ? 

Secondly,  all  these  four  marks  do  meet  in  the  matters  of 
fact  which  are  recorded  in  the  Gospel,  of  our  Saviour.  For  the 
two  first : the  miracle  of  feeding  three  thousand  at  one  time ; 
five  thousand  were  converted  at  one  time  by  what  they  had 
seen — miracles  that  were  done  publicly  and  before  their  own 
eyes.  Then  for  the  two  last : Baptism,  the  Lord’s  Supper, 
were  instituted  as  memorials  of  what  was  then  done ; and  the 
institution  of  the  Ministry,  which  has  continued  by  a regular 
succession  to  this  day,  in  all  which  respects  the  matters  of  fact 
of  the  Gospel  narrative  as  completely  fulfil  the  four  rules  as 
those  that  are  related  of  Moses. 

III.  The  matters  of  fact  of  Mahomet  and  the  fabled  dei- 
ties, do  all  want  these  four  marks. 

First,  Mahomet  did  not  claim  in  his  day  to  have  performed 
any  miracles. 


404 


LOGIC.  — APPENDIX. 


Secondly,  those  that  are  told  of  him  want  the  first  two 
rules ; they  were  not  performed  in  the  presence  of  any  one, 
and  we  have  only  his  word  for  them. 

The  same  is  to  be  said  of  the  fables  of  the  Heathen  gods. 

It  is  true  that  the  Heathen  deities  had  their  priests.  They 
had  also  feasts  and  games,  and  other  institutions  in  memory 
of  them.  But  all  these  want  the  fourth  mark,  they  were  not 
instituted  at  the  time  of  the  occurrence  of  the  events  which 
they  claim  to  commemorate ; and  their  priests  were  not  ap- 
pointed by  the  gods,  but  only  by  others  in  honor  of  them. 
And  therefore  these  orders  of  priests  are  no  evidence  to  the 
truth  of  the  matters  of  fact  which  are  reported  of  their 
gods. 

IV.  Now  to  apply  what  has  been  said.  You  may  challenge 
all  the  Deists  in  the  world  to  show  any  action  that  is  fabulous, 
which  has  all  the  four  rules  or  marks  before  mentioned.  No, 
it  is  impossible.  And  (to  resume  a little  what  has  been  spoken 
of  before)  the  histories  of  Exodus,  and  the  Gospel,  never  could 
have  been  received,  if  they  had  not  been  true ; because  the 
institution  of  the  Priesthood  of  Levi,  and  of  Christ  ; of  the 
Sabbath,  of  the  Passover,  and  of  Circumcision ; of  Baptism, 
and  of  the  Lord’s  Supper,  &c.,  are  there  related  as  descend- 
ing all  the  way  down  from  those  times,  without  interruption. 
And  it  is  full  as  impossible  to  persuade  men  that  they  had 
been  circumcised  or  baptized — had  circumcised  or  baptized 
their  children  — had  celebrated  passovers,  sabbaths,  sacra- 
ments, &c.,  under  the  government  and  administration  of  a cer- 
tain order  of  priests,  if  they  had  done  none  of  these  things,  as 
to  make  them  believe  that  they  had  gone  through  seas  upon 
dry  land,  seen  the  dead  raised,  &c.  And  without  believing 
these,  it  was  impossible  that  either  the  Law  or  the  Gospel 
could  have  been  received. 


§ 8.  Mr.  Webster’s  Argument  in  the  Girard  Will  Case. 

This  Will  devises  a certain  sum  of  money  to  be  appro- 
priated to  the  erection  and  support  of  a College  (10).* 

The  first  question  is  whether  this  devise  can  be  sustained 

* These  numbers  in  parentheses  refer  to  the  page  in  the  printed  speech, 
from  which  the  statements  preceding  them  are  taken. 


EXAMPLES  FOR  CRITICISM. 


405 


otherwise  than  as  a charity.  If  the  devise  he  a good  limita- 
tion at  law,  if  it  require  no  exercise  of  the  favor  which  is 
bestowed  upon  privileged  testaments,  there  is  already  an  end 
to  the  question — this  point  is  conceded. 

The  devise  is  void  according  to  the  general  rules  of  law, 
on  account  of  its  not  mentioning  the  persons  to  whom  the  be- 
quest is  made. 

The  bequest  must  stand  then,  if  it  stand  at  all,  on  the  pecu- 
liar rules  which  equitable  jurisprudence  applies  to  charities. 

But  I maintain  that  neither  by  judicial  decisions,  nor  by 
correct  reasoning  on  general  principles,  can  this  devise  or  be- 
quest be  regarded  as  a charity; (11)  because, 

It  is  derogatory  to  the  Christian  Religion. 

It  tends  to  weaken  men’s  reverence  for  that  Religion,  and 
their  conviction  of  its  authority  and  importance ; and,  there- 
fore, it  tends  in  its  general  character  to  mischievous  and  not 
to  useful  ends. 

The  College  is  founded  to  promote  infidelity,  and  a gift  or 
devise  for  such  objects  is  not  a charity  (12). 

The  object  of  this  bequest  is  against  the  public  policy  of 
the  State ; therefore  the  devise  ought  not  to  be  allowed  to 
take  effect. 

These  are  the  two  propositions  which  it  is  my  purpose  to 
maintain  on  this  part  of  the  case  (12). 

The  Will  excludes  all  Ministers  of  the  Gospel  from  the 
College  (13). 

There  is  no  Christian  charity  that  excludes  the  Minis- 
try (16). 

It  has  so  been  understood  from  the  time  of  Constantine 
down  to  our  own  (16). 

The  opening  counsel  admitted  that  there  is  no  charity 
without  Christianity  (19),  and  I maintain  that  wherever 
the  authority  of  God  is  disowned,  the  duties  of  Chris- 
tianity derided,  and  its  Ministers  shut  out,  there  can  be 
no  charity  (19,  20). 

He  who  rejects  the  ordinary  means  of  accomplishing  an 
end  means  to  defeat  that  end  itself,  or  else  he  has  no  meaning ; 
this  is  true  even  if  the  means  be  but  of  human  appointment, 
althpugh  the  end  rested  on  divine  authority.  But  if  the 
means  be  of  divine  authority  also,  then  the  rejection  of  them 
is  direct  rejection  of  that  authority  (30). 


406 


LOGIC. — APPENDIX. 


But  nothing  is  more  certain  in  Christianity,  than  that  the 
Author  of  the  Christian  Religion  Himself  did  appoint  a Chris- 
tian Ministry. 

He  who  does  not  believe  this  cannot  believe  the  rest  (31). 

This  Ministry  have  continued  to  our  day,  and  gone  over 
the  whole  world  performing  their  work.  Nowhere  has  any 
part  of  the  globe  been  Christianized  without  the  Ministry.  It 
is  therefore  idle  mockery  to  pretend  that  that  man  has  any 
respect  for  the  Christian  Religion  who  derides  and  rejects  its 
Ministers  (32). 

In  the  next  place  this  scheme  of  education  is  derogatory  to 
Christianity,  because  it  proceeds  upon  the  presumption  that 
Christianity  is  not  the  only  true  foundation,  or  any  necessary 
foundation  of  morals. 

So  the  world  has  not  thought. 

The  Word  of  God  declares  otherwise  in  the  Decalogue  (34). 

Christ  taught  otherwise  (35). 

Reason  and  human  nature  teach  otherwise  (35,  36). 

Again,  the  Will  excludes  the  observance  of  the  Christian 
Sabbath. 

But  the  Christian  Sabbath  is  a part  of  Christianity.  This 
is  admitted  by  all  Christians  (37),  and  the  Will  excludes  the 
means  for  observing  the  Sabbath  (37,  38). 

And  where  the  Christian  Sabbath  is  not  observed,  there  is 
no  public  worship  of  God. 

But  the  reasons  assigned  for  the  exclusion  of  Christianity 
from  the  College,  are  still  more  derogatory  to  Christianity. 

They  are  that  the  evils  resulting  from  the  diversity  of 
opinions  and  sects,  is  greater  than  the  good  which  Christianity 
itself  produces ; whence  he  infers  that  we  should  cut  up  Chris- 
tianity by  the  roots  (42). 

But  this  mode  of  reasoning,  if  it  were  allowed,  would 
destroy  men’s  social  relations  and  all  human  institutions  (46, 
47). 

But  there  is  a settled  policy  of  the  State  of  Pennsylvania ; 
this  is  not  denied  ; and  Christianity  is  a part  of  that  policy. 

Any  school  or  system  of  education  which  is  contrary  to 
that  policy,  cannot  be  sustained  by  the  State  (65). 

The  Courts  of  Pennsylvania  have  declared  that  a charitable 


EXAMPLES  FOE  CRITICISM. 


407 


bequest  which  counteracts  the  public  policy  of  the  State  can- 
not be  sustained  (67).  [The  case  of  Methodist  Church  vs. 
Remington  and  the  8th  of  Johnson,  p.  291.] 


§ 9.  Mr.  Dana’s  Argument  in  the  Ellsworth  School  Case. 

This  was  a suit  brought  by  Laurence  and  Bridget  Donahoe 
against  Richards  and  others,  Superintending  Committee  of 
Schools,  claiming  damages  of  the  Committee  for  having  ex- 
cluded the  Plaintiffs  from  the  benefit  of  the  common  schools, 
by  making  the  reading  of  the  Bible,  in  the  common  English 
Version,  obligatory  upon  all  the  pupils.  The  Plaintiffs  being 
Roman  Catholics  could  not  comply,  on  grounds  of  conscien- 
tious scruples. 

This  is  a novel  suit ; there  is  no  one  like  it  in  the  Reports. 

The  general  principle  of  law  is,  “ that  a public  officer  exer- 
cising a discretion,  judicial  in  its  character,  cast  upon  him  by 
the  law,  is  not  liable  to  private  actions  for  damages,  unless  he 
acts  in  bad  faith  or  from  malice.” 

But  in  this  case  it  is  not  pretended  that  there  was  malice 
or  bad  faith  (6). 

By  the  constitution  and  laws  of  Maine  it  is  the  duty  of  the 
Committee,  “ to  direct  the  general  course  of  instruction,  and 
what  books  shall  be  used  in  the  respective  schools.”  In  the 
exercise  of  this  authority,  the  Committee  continued  the  use  of 
the  Bible  in  the  common  English  Version  (7). 

By  authority  of  the  State  also  they  have  power  to  expel 
from  any  school,  any  pupils  who  shall  not  comply  with  the 
regulations  which  they  have  made  (7). 

Now  the  point  whether  the  Defendants  in  this  suit  are  lia- 
ble has  never  been  decided. 

But  in  the  case  of  Wheeler  vs.  Patterson,  1 N.  H.  88,  it 
was  decided  that  Selectmen  of  a town,  were  not  liable  for 
refusing  a man  his  privilege  of  voting,  even  though  they  were 
wrong  in  their  act,  “ so  long  as  their  motives  are  pure  and 
untainted  with  fraud  and  malice.” 

In  the  case  of  Griffin  vs.  Rising,  11  Met.  339,  it  was  held 
that  Assessors  were  not  liable  for  refusing  to  tax  a man,  al- 
though he  lost  his  vote  thereby,  on  the  ground  that  they  “ are 


408 


LOGIC.— APPENDIX. 


exempted  from  liability  for  damages  when  acting  with  in- 
tegrity.” 

In  Allen  vs.  Blunt,  3 Story  141,  it  was  held  that,  “ where 
a particular  duty  is  confided  to  a public  officer,  to  be  exercised 
by  him  at  his  discretion,  upon  an  examination  of  facts,  of 
which  he  is  made  the  appropriate  judge,  his  decision  is  con- 
clusive.” 

In  7 Howard  89,  and  12  Howard  390,  it  was  held  that  the 
commander  of  a ship  was  not  responsible  for  the  punishment 
of  a marine,  though  he  were  innocent,  so  long  as  he  did  it  not 
from  malice,  and  that  he  was  not  responsible  for  error  of  law, 
or  in  his  judgment  of  facts  if  he  acted  in  good  faith. 

All  these  cases  are  analogous  to  the  one  before  the  Court. 
The  only  exception  is  the  case  of  Lincoln  vs.  Hapgood.  This 
decision,  however,  has  been  overruled. 

But  not  only  are  the  defendants  not  liable  for  damages  in 
this  suit.  The  continuance  of  the  use  of  the  Bible  is  a rea- 
sonable exercise  of  their  discretionary  power. 

It  has  always  been  used  in  the  schools  of  Maine. 

The  Defendants  are  obliged  by  law  to  see  that  the  princi- 
ples of  morality  and  all  the  virtues  shall  be  taught  in  the 
schools.  But  how  can  principles  of  morality  be  taught  except 
on  the  basis  of  religion  ? A system  of  morality  not  founded 
on  religion  is  not  morality,  but  only  a system  of  self-interest. 

The  objection  however  is  not,  they  say,  to  the  Bible,  but 
to  our  English  Version  of  it. 

But  “ great  portions  of  the  translation  were  made  by  men 
in  the  bosom  of  the  General  Church  before  the  Reformation.” 
Testimony  to  its  accuracy  has  been  borne  by  learned  men  of 
the  Roman  Church. 

As  a fountain  of  pure  idiomatic  English  it  has  no  equal  in 
the  world.  From  it  we  derive  our  household  words.  Hence 
as  a preparation  for  life,  an  acquaintance  with  the  common 
English  Bible  is  indispensable,  while  the  Romish  Version  is 
un-English. 

But  the  effect  of  this  objection  is  to  exclude  the  Bible 
altogether.  Each  denomination  has  a translation,  or  at  least 
prejudices  and  peculiar  views  of  its  own.  If  one  is  to  insist 
on  his  version,  others  will ; and  all  will  be  excluded.  The 
question,  therefore,  is  whether  the  Bible  shall  be  read  at  all 
or  not. 


EXAMPLES  FOE  CRITICISM. 


409 


It  only  remains  to  consider  the  constitutional  objections 
against  the  law  under  which  the  Committee  acted. 

The  power  to  regulate  schools  and  determine  what  studies 
shall  be  pursued,  and  what  books  read,  must  be  lodged  some- 
where. The  Constitution  of  Maine  gives  the  Legislature 
power  “ to  make  and  establish  all  reasonable  laws  and  regula- 
tions for  the  defence  and  benefit  of  the  people,  not  repugnant 
to  the  Constitution  of  Maine,  or  to  that  of  the  United  States.” 
And  if  this  power  to  select  books,  and  suspend  or  refuse  chil- 
dren for  disobedience,  were  not  expressly  given  in  the  Consti- 
tution, it  would  be  implied  in  the  necessity  of  the  case  (Sher- 
man vs.  Charlestown,  8 Cush.  161 ; and  Spear  vs.  Cummings, 
22  Pick.  223). 

It  is  said  that  the  schools  are  public,  and  that  all  resident 
tax-payers  have  a vested  right  in  them. 

But  this  right  must  be  enjoyed  subject  to  restrictions  and 
limitations,  necessary  for  the  good  and  rights  of  others.  This 
does  not  subject  one  denomination  to  another,  but  the  choice 
of  a few  to  the  good  of  the  many. 

The  only  constitutional  question  worthy  of  attention,  is 
that  which  arises  from  the  clause  which  declares  that  “ no  one 
shall  be  hurt,  molested,  or  restrained  in  his  person,  liberty,  or 
estate  for  his  religious  opinions.” 

This  clause  was  intended  to  guard  against  persecution, 
directed  against  person  or  property.  But  there  is  no  such 
persecution  in  this  case ; whatever  inconvenience  may  have  been 
suffered,  is  the  incidental  and  indirect  consequence  of  the 
opinions  which  the  Plaintiffs  choose  to  hold. 

But  if  they  were  “ hurt  or  molested,”  in  the  sense  of  the 
Constitution,  still  the  act  of  the  Committee  is  not  unconstitu- 
tional. 

It  is  a constitutional  provision,  for  instance,  that  no  man’s 
property  shall  be  taken  for  public  uses  without  compensation. 
And  yet  the  Legislature  has  full  power  to  regulate  the  manner 
in  which  men  shall  use  and  enjoy  their  property,  so  as  to  pre- 
serve the  rights  of  the  public.  In  this  exercise  of  legislative 
power,  a man’s  property  may  sometimes  be  much  diminished, 
or  even  destroyed,  and  he  have  no  remedy. 

In  the  Warren  Bridge  case  it  was  established  that  the 
State  may  impair  or  destroy  the  value  of  an  existing  franchise 
for  the  public  good,  and  that  no  compensation  need  be  made, 

18 


410 


LOGIC. APPENDIX. 


if  it  be  not  confiscated  or  abolished.  The  daily  making  of 
highways,  railroads,  and  canals  for  the  public  good,  is  con- 
stantly impairing  the  value  of  some  private  property,  and  in 
some  cases  totally  destroying  it,  and  yet  no  compensation  is 
made. 

In  the  case  of  Tewksbury  it  was  held  (11  Met.  55)  that  the 
State  might  prohibit  Mr.  T.  from  taking  sand  from  his  own 
beach.  So  in  Alger’s  case  (7  Cush.  53),  burials  in  cities  may 
be  prohibited  without  compensating  the  owners  of  vaults  for 
their  loss,  however  costly  or  valuable  they  may  have  become. 
The  Sunday  laws  also  are  held  to  be  constitutional,  although 
the  Jews,  by  reason  of  their  religious  profession,  lose  one  sixth 
of  their  working  life,  and  are  “ hurt  and  restrained  in  their 
liberty  and  estate,”  and  put  to  an  inequality  with  Christians. 

The  Constitution  prohibits  religious  tests  as  qualifications 
to  office.  Y et  all  judicial  officers  are  required  to  administer 
oaths,  although  the  Quakers  regard  the  taking  of  oaths  as  un- 
lawful. 

Hence  we  must  conclude  that  the  power  of  the  Committee 
is  not  rendered  unconstitutional,  by  the  mere  fact  that  it  inci- 
dentally operates  to  the  disadvantage  of  an  individual  who,  by 
his  opinions  or  preferences,  has  put  himself  in  opposition  to 
the  laws  of  the  land  and  the  acts  of  its  legitimate  authorities. 


INDEX 

OF  SUBJECTS  AND  OF  THE  TECHNICAL  TERMS  OCCURRING 
IN  THE  WORK. 


Abscissio  Infiniti  241,  its  uses  241, 
242. 

Absolute  truth,  proved  only  by 
Demonstration  325. 

Abstract,  knowledge  of  the,  subse- 
quent to  that  of  the  concrete  361. 

Abstract  Terms  explained  14. 

Abstraction  what  215. 

Acategorematic  Terms  13. 

Accidents  separable  and  insepara- 
ble 19,  predicated  of  all  subjects 
56,  Fallacy  of  191. 

Accidental  Properties  may  be- 
come Formal  222,  may  become 
Material  284,  may  become  Essen- 
tial 310. 

Achilles  and  the  Tortoise,  sophisms 
of  235  n. 

Acquisition  of  knowledge  begins 
with  the  individual  and  concrete 
361. 

Addition,  the  Principle  of  234. 

Adequacy  of  Propositions  55. 

Adjectives,  their  logical  force  48. 

Affirmation,  grounds  of  102. 

Affirmative  Judgments  classify 
their  subject  54,  how  related  to 
Negative  61,  do  not  distribute  the 
Predicate  67,  substitution  of  terms 
in  76. 

Agassiz  Prof,  view  of  Classification 
and  Induction  312  n. 


Aldrich’s  account  of  the  Predica- 
bles 19  n. 

Algebra,  a series  of  Methods  of  In- 
vestigation in  Discrete  Quantity 
234. 

Alternate  Conceptions  15. 

Alternate  Species  27,  used  as 
subjects  56,  constitute  coordinate 
terms  in  Disjunctive  Judgments 
100. 

Amotion  of  a Proposition,  what 
172  n. 

Ambiguous  Middle  what  189,  vari- 
ous forms  of  190. 

Ampere’s  Classification  of  the  Sci- 
ences criticised  340. 

Analogous  Spheres  20. 

Analogy  33  and  249  n.,  proved  by 
Affirmative  Premises  in  the  2d 
Figure  124,  as  a Method  of  In- 
vestigation 249,  Aristotle’s  and 
Whately’s  definition  of  249  n., 
stops  short  of  an  Induction  257, 
its  use  257-259,  argument  from 
319,  its  value  320,  as  a means 
of  removing  antecedent  objec- 
tions 321. 

Analysis,  what  215,  different  kinds 
of  215,  proximate  and  ultimate 
or  last  216,  must  precede  synthe- 
sis 218,  as  a Method  of  Investi- 
gation 243,  of  conceptions  and  of 


412 


INDEX. 


things,  logical  and  physical  243, 
certainty  of  its  results  244  et  seq„ 
enables  us  to  see  Implied  proper- 
ties 248. 

Analytic  Method  of  Teaching  362, 
based  upon  the  Natural  Classifi- 
cation 363. 

Analytic  Judgments  203,  do  not 
add  to  our  knowledge  203,  a priori 
206. 

Antecedence  not  Causality,  though 
implied  in  it  259,  proved  by  In- 
duction 260. 

Antecedent  in  a Conditional  Judg- 
ment 91,  ground  of  the  truth  of 
the  Consequent  171. 

Antecedents  in  Nature,  simple  and 
complex  264. 

Antecedent  Probability  and  im- 
probability with  reference  to  dif- 
ferent totalities  89. 

Antithetic  Terms  41. 

Apodictic  or  Necessary  Judgments 
60,  their  relation  to  the.  Assertives 
as  used  in  Formula  63. 

Appeal  to  facts  303. 

Approach  progressive  324. 

Argument  analyzed  7,  from  Con- 
ceptions 281,  from  Principles  290, 
from  Authority  293,  from  Facts 
303,  by  Induction  304,  by  Exam- 
ple 316,  by  Analogy  319,  by  con- 
currence of  Circumstances  and 
Testimony  322,  by  Progressive 
Approach  324,  Argumentnm  ad  Ig- 
narantiam  326,  from  Exceptions 
330,  ad  Hominem.  336,  ad  Veream- 
diam  336,  ad  Invidiam  337,  distin- 
guished from  Assertion  374,  and 
Artifices  374. 

Aristotle  the  founder  of  Logic  1, 
attributes  its  origin  to  Zeno  2,  his 
Categories  34  n.,  his  Dictum  124  n., 
his  list  of  Sophisms  or  Fallacies 
184  n.,  his  true  Conclusion  from 
false  Premises  187  n.,  his  defini- 
tion of  Induction  249  n.  and 
304  n.,  his  Notions  311,  Classifi- 
cation of  the  Sciences  339,  Meta- 
basis 379  n. 

Arithmetic  a series  of  Methods  of 


Investigation  in  Discrete  Quan- 
tity 234. 

Article  not  used  before  words  de- 
noting Genera  52. 

Artifices  to  be  distinguished  from 
Formula  and  from  Fallacies  192, 
from  Arguments  374. 

Arts,  the  Faculty  of  339. 

Assertion  to  be  distinguished  from 
Argument  374. 

Assertive  Judgments  61,  their  re- 
lation to  the  Formula  63. 

Authority  proved  by  Testimony 
231,  Arguments  from  293,  our 
only  ground  of  proof  in  some 
cases  294. 

Average,  a Method  of  Investigation 
237,  its  various  uses  238,  239, 
240. 

Axioms  290  note , how  proved  278. 

Bacon’s  Experimentum  Crucis  273, 
Classification  of  the  Sciences  340. 

Barbara,  Syllogism  in  119,  all  Syl- 
logisms whose  names  begin  with 
B may  be  reduced  to  127. 

Baroko  120,  reducible  to  Barbara 
127,  128,  to  Ferio  129. 

Beautiful,  the  Idea  of  the,  as  de- 
termining Methods  199,  its  rela- 
tion to  the  Useful  201. 

Begging  the  Question,  Fallacy  of 
186. 

Boicardo  121,  may  be  reduced  to 
Barbara  127,  129,  to  Darii  129. 

Botany  cited  as  an  illustration  of  the 
Progress  of  Scientific  Classification 
358. 

Bramantip  122,  may  be  reduced  to 
Barbara  127,  128,  peculiarity  of 
in  the  resolution  of  Sorites  141. 

Butler  Bishop,  Method  of  in  the 
Analogy  321,  334. 

Calculation,  Methods  of  in  Dis- 
crete Quantity  233. 

Calculus,  a series  of  Investigations 
in  Discrete  Quantity  234. 

Camenes  122,  may  be  reduced  to 
Celarent  127. 


INDEX. 


413 


Camestres  120,  may  be  reduced 
to  Celarent  127. 

Categorematic,  terms  when  said  to 
be  13. 

Categorics  13,  of  Aristotle  34  n., 
of  Kant  34  n. 

Categoric  Judgments  44,  Pure, 
Comparative,  and  Probable  45, 
make  a Classification  50,  simple 
and  complex  .77,  Compound,  Co 
pulative  80,  Causal  81,  Discretive 
81,  Conditional  82,  Disjunctive  82, 
Exceptive  and  Exclusive  83,  Com- 
parative 84. 

Categorical  Syllogisms  include 
three  Propositions  and  three 
Terms  108,  names  of  Terms  and 
Premises  in  108,  109,  number  and 
names  of  122,  indirect  conclusions 
of  123,  conversion  of  124,  Modals 
in  131,  Compound  or  Sorites  138, 
Compound  Propositions  in  149. 

Causal  Propositions  81,  are  pro- 
perly Enthymemes  150,  how  com- 
pleted 150. 

Causality  something  more  than 
Antecedence  259,  not  proved  hy 
Induction  260,  three  conditions 
required  261,  often  depends  upon 
the  Mode  of  the  Substance  263, 
often  depends  upon  the  complex- 
ity of  the  Antecedent  264. 

Cause  absolute  29,  and  effect  alter- 
nate conceptions  30,  relative  30, 
primary  and  secondary  30,  effi- 
cient, occasional,  material,  formal, 
final,  and  negative  30,  transient, 
permanent,  and  immanent  32,  in 
Nature  only  secondary  260,  called 
also  Instrumental  261,  Substan- 
tial and  Modal  259,  must  be  a 
substance  261,  causa  vera  and 
causa  sufficiens  262,  adequate  and 
homogeneous  263,  four  kinds  of 
words  denoting  Causes  264,  when 
to  be  given  in  Instruction  365. 

Celarent  119,  all  Syllogisms  begin- 
ning with  C may  be  reduced  to  1 27. 

Certainty  absolute  211,  physical 
212,  moral  213,  in  regard  to 
masses  of  men  213. 


Cesare  120,  reduced  to  Celarent 
128. 

Chain  Syllogism  or  Sorites  138. 

Chances  favorable  and  unfavorable 
87,  in  the  same  and  in  different 
Events  165. 

Circumstances,  facts  regarded  as 
215,  argument  from  322,  its  pro- 
per sphere  323. 

Class-conceptions  what  205,  of 
the  Creative  Mind  the  basis  of 
Induction  306. 

Classification  implied  in  all  Cate- 
goric Judgments  50,  Principle  of 
extends  to  more  than  three  grades 
51,  based  upon  accidental  proper- 
ties 53,  become  jests  54,  Formula 
of  146,  made  at  the  second  ob- 
servation 221,  and  a new  one  at 
the  next  221,  the  basis  of  Induc- 
tion 250,  the  principle  of  changes 
in  the  progress  of  science  252, 
357,  a new  one  required  when  the 
exceptions  become  numerous  256, 
not  properly  based  upon  variable 
properties  256,  of  the  Sciences  338, 
Plato’s,  Aristotle’s,  and  the  Scho- 
lastic 339,  Bacon’s,  Locke’s,  Cole- 
ridge’s, and  Ampere’s  340,  Comp- 
te’s  341,  a new  one  342  et  seq., 
character  of  the  Primary  356, 
necessity  for  the  transition  from 
Natural  to  Scientific  357,  test  of 
the  perfection  of  357,  358,  illus- 
trated from  Botany  358. 

Cognition  7,  9,  distinguished  from 
Conception  10. 

Collective  Terms  distinguished 
from  General  17,  may  not  be  pre- 
dicated of  the  individuals  18. 

Commissions  conveying  authority 
how  to  he  interpreted  300. 

Common  Sense,  a ground  of  belief 
294. 

Comparative  Judgments  45,  do 
not  include  the  Subject  in  the 
Sphere  of  the  Predicate  84,  con- 
tain three  terms  85,  of  seven  va- 
rieties 84-87,  conversion  of  86,  in 
Syllogisms  151. 

Comparative  Syllogisms,  not  the 


414 


INDEX. 


same  as  pure  Categoricals  151, 
simple  comparatives  152,  the  con- 
ditions of  their  validity  154,  in 
which  intensity  is  regarded  as 
cause  155,  of  manner,  time,  place, 
&c.  156. 

Comparisons,  imply  three  terms  85, 
of  equality  and  inequality,  and  of 
greater  and  of  less  intensity  85, 
of  time,  place,  &c.  86. 

Composition,  Fallacy  of  190. 

Complex  Propositions  reducible  to 
simple  incomplex  84. 

Compound  Categorical  Proposi- 
tions reducible  to  simple  complex 
84. 

Compound  Conditionals  96,  174. 

Comprehended  Sphere  always  the 
Subject  111. 

Comprehending  Sphere  always  the 
Predicate  111. 

Comprehension  of  Terms  14. 

Comprehensive  Quantity  deter- 
mines the  intensive  60,  of  three 
degrees  60. 

Comprehensiveness  of  terms  ex- 
clusiveness of  matter  51. 

Compte’s  Classification  of  the  Sci- 
ences 34 1 . 

Conception  7,  9,  adequate  and  in- 
adequate 10,  of  Ideas,  how  made 
adequate  11,  of  the  Impossible  12, 
the  relations  of  13,  the  sphere  and 
matter  of  14,  matter  determines 
the  sphere  15,  Alternate  15,  dis- 
tinguished from  facts  214.  manner 
of  passing  from  one  mind  to  an- 
other 216,  347,  Analysis  of  244, 
cannot  be  conveyed  from  mind  to 
mind  as  wholes  348,  reconstructed 
by  the  person  receiving  it  349, 
none  that  cannot  be  defined  351, 
Ultimate  and  Primary  355,  imply 
previous  perceptions  356,  made 
distinct  by  the  Essentia,  definite 
by  the  Differentia  366. 

Concessions  a ground  of  proof  294. 

Conclusion,  what  7,  107,  no  af- 
firmative in  the  2d  Figure  113,  no 
universal  in  the  3d  114,  quantity 
and  quality  of  determined  by  the 


Premises  115,  indirect  123,  direct 
123,  compound  149,  true  from 
false  Premises,  Aristotle’s  account 
of  187  n.,  when  proved  280,  as 
determining  wholes  in  argumenta- 
tion 375. 

Concrete,  knowledge  begins  with 
objects  in  the  361. 

Concrete  Terms  14. 

Concurrence  of  fjacts  or  of  testi- 
mony, what  322,  its  value  323. 

Conditional  Judgments  44,  imply 
categoric  45,  three  terms  and  two 
copulas  91,  members  of  91,  depend 
upon  the  Sequence  92,  compound- 
ed with  Disjunctives  102. 

Conditional  Modals  79,  may  be- 
come Differential  136. 

Conditional  Propositions  82,  91, 
compound  96,  continuous  96. 

Conditional  Syllogisms,  not  all 
that  contain  conditional  judg- 
ments are  so  171,  methods  of 
completing  172,  method  for  find- 
ing the  Sequence  173,  may  be 
completed  into  a categorical  174, 
with  four  terms  174,  compound 

174,  continuous  175,  with  com- 
pound consequents  or  antecedents 

175. 

Conjecture,  what  218. 

Conjugation  of  the  Verb  as  an  illus- 
tration of  Definition  354. 

Connotative  Terms  14,  how  predi- 
cable 42. 

Consciousness,  a means  of  Investi- 
gation 224. 

Consequent  in  conditional  judg- 
ments 91,  the  denial  of  destroys 
the  Antecedent  172. 

Construction,  object  and  method 
of  347. 

Constructive  Method  with  Condi- 
tionals 172. 

Contingent  Matter  205,  judg- 
ments in  a posteriori  206,  in  all 
realities  of  being  209,  how  known 
210,  Analysis  as  a means  of  In- 
vestigation in  244. 

Continuous  Conditionals  96. 

Continuous  Quantity  22,  limits 


INDEX. 


415 


and  terms  in  23,  39,  axioms  of 
152. 

Contradictio  in  adjectis  3T5. 

Contradiction,  principle  of,  a ground 
of  affirmation  103. 

Contradictory  Terms  41,  how  pre- 
dicable 42. 

Contradictory  Judgments  cannot 
both  be  false  in  the  same  matter 
70. 

Contraries,  a means  of  Investiga- 
tion 250. 

Contrariety  33. 

Contra-position  of  Judgments  71, 
by  means  of  Negatives  73. 

Contrary  Judgments  cannot  both 
be  true  in  the  same  matter  70. 

Contrary  Terms  40,  how  predica- 
ble 42. 

Conversion  of  Propositions  74,  sim- 
ply and  by  limitation  75,  of  O 75, 
of  Comparatives  86,  of  Syllo- 
gisms 124. 

Conveying  words  of,  bow  to  be  in- 
terpreted 299. 

Coordinate  Divisions  25,  parts  26. 

Copula,  affirmative  and  negative  7, 
its  force  48,  its  effect  in  pure  cate- 
goricals  49,  its  form  49,  real  and 
designed  effect  of  50. 

Copulative  Propositions  80,  may  be 
resolved  into  simple  Propositions 
80,  danger  of  them  including  er- 
ror 81. 

Counting,  a method  of  Investiga- 
tion 234. 

Critic  the,  position  occupied  by  369. 

Criticism,  principles  of,  the  same 
as  those  of  Construction  369, 
starting  point  of  370. 

Damascene,  St.  John,  on  Analysis 
215  n. 

Darii  119. 

Datisi  121,  mav  be  reduced  to  Da- 
rii 127. 

Deduction,  compared  with  Induc- 
tion 276  ».,  as  a method  of  Proof 
290,  the  method  of  application  of 
Sciences  291,  and  of  completing 
Sciences  292, 


Deductive  Judgments,  how  differ- 
ent from  Intuitive  106. 

Definition  33,  may  be  predicated 
of  any  object  55,  used  instead  of 
the  term  131,  analyzes  conceptions 
349,  when  adequate  349,  353, 
verbal  and  real  350,  may  be 
given  to  all  conceptions  351, 
some  difficulties  noted  352,  Ac- 
cidental, Physical,  and  Meta- 
physical 353,  negative,  what  353 
n.,  the  conjugation  of  verbs  a 
definition  354,  may  need  to  be 
defined  355,  must  always  refer 
to  the  natural  classification  359, 
use  of  negative  in  instruction 
365  n. 

Demonstration,  popular  and  strict 
senses  of  the  word  281,  from  the 
force  of  terms  282,  based  on  ety- 
mology 283,  not  used  in  Contingent 
Matter  284,  287,  the  basis  of  all 
Sciences  285,  290,  gives  Universal 
Conclusions  from  Individual  Pre- 
mises 286,  based  upon  Hypothe- 
ses 288. 

Demoniacal  Possessions,  how  prov- 
able 227  n. 

Description,  what  34,  as  a means 
of  conveying  conceptions  351,  does 
not  furnish  the  matter  for  the  con- 
ception 355. 

Destructive  Method  with  Condi- 
tionals 172. 

Devey’s  Logic  cited  292  n. 

Diagrams  in  Mathematics  as  repre- 
senting conceptions  207. 

Dictionaries  a Testimony  to  the 
meaning  of  words  232,  gives  ver- 
bal definitions. 

Dictum  of  Aristotle  124  n.,  of  Lam- 
bert 125  n. 

Difference  in  kind  and  in  degree 
32. 

Differently  must  bear  some  rela- 
tion to  the  Essentia  51,  may  be 
merely  relative  Properties  351  n., 
the  same  in  different  genera  con- 
stitute Kecurring  Species  359, 
always  necessary  in  Instruction 
364. 


410 


INDEX. 


Differential,  Modals  78,  may  be 
converted  into  Conditional  136. 

Dilemma  102,  seldom  needs  comple- 
tion 179,  its  various  forms  179- 
181. 

Dimaris  122,  may  be  reduced  to 
Darii  127. 

Disamis  121,  may  be  reduced  to 
Darii  127. 

Discrete  Quantity  22,  terms  and 
limits  of  22,  applied  to  Logical 
and  Continuous  23,  terms  in  38, 
gives  validity  to  syllogisms  other- 
wise invalid  152,  two  axioms  of 
157,  applied  to  continuous  in  cate- 
gorical Syllogisms  158,  affords  no 
distributed  terms  159,  its  effect 
when  applied  to  one  Premise  only 
162. 

Discretive  Propositions  81,  in  Syl- 
logisms 150. 

Disjunctive  Judgments  44,  imply 
categoric  45,  depend  upon  the  Ex- 
cluded Middle  97,  with  four  terms 
101,  compounded  with  condition- 
als 102,  convertible  into  condi- 
tionals 102,  comprehensive  and 
divisive  175. 

Disjunctive  Propositions  82. 

Disjunctive  Syllogisms  175,  com- 
prehensive and  divisive  176,  Syl- 
logisms not  always  disjunctive 
when  there  is  a disjunctive  Pre- 
mise 176,  the  Major  Premise  dis- 
junctive 177,  how  completed  mo- 
dus tottente  pawns,  and  pownte  tol- 
lens  177,  with  more  than  two  mem- 
bers 178,  divisive,  how  completed 
178. 

Disparate  Parts  26,  do  not  consti- 
tute an  Excluded  Middle  100. 

Distributer  Terms  40,  in  judg- 
ments 64,  by  nature,  by  signs  65, 
by  position  67. 

Division  21,  of  three  kinds  24,  prin- 
ciple of  25,  coordinate  and  subor- 
dinate 26,  canons  of  28,  fallacy 
of  190,  numerical  236,  of  general 
subject  in  teaching  360,  into  coor- 
dinate parts  if  possible  361,  into 
alternate  species  361. 


Divisive  Judgments  175. 

Divisive  Principle  25. 

Divinity,  the  Faculty  ofj  in  the  Uni- 
versities 339. 

Each,  a sign  of  a distributed  subject 
in  a Proposition  66. 

Edicts  restraining  liberty,  how  to 
be  interpreted  300. 

Effect  and  Cause  alternate  concep- 
tions 30,  immediate  and  remote, 
direct  and  accidental,  designed 
and  undesigned  32,  investigation 
of  271,  273,  when  to  be  given  as 
an  element  of  Instruction  365. 

Elimination,  when  practicable  265, 
depends  upon  four  axioms  266, 
first  Method  of  Elimination  267, 
second  and  third  268,  fourth  269, 
fifth  271. 

End,  Method  supposes  one,  hut  does 
not  furnish  it  196,  determines 
the  selection  of  matter  in  Instruc- 
tion 367,  369,  in  determining 
wholes  375. 

Enthymemes,  what  142,  of  four  kinds 
143,  with  three  terms  may  be 
completed  into  Syllogisms  143, 
with  four  terms,  completed  into 
Sorites  144,  may  be  stated  as  Con- 
ditionals 173. 

Epichirema  148. 

Epi-syllogism  148. 

Equality,  comparisons  of  85,  mean- 
ing of  in  Algebra  157  re. 

Essence  of  an  object  16,  different 
senses  of  the  word  16  re. 

Essentia  of  a Genus  17,  always  ne- 
cessary in  Instruction  364,  makes 
the  conception  distinct  366. 

Ethnology,  cited  as  an  illustration 
of  the  principle  of  classification 
357. 

Exact  Sciences,  what  and  why  so 
called  342  re. 

Example,  argument  from  316,  an 
induction  from  a single  fact  318, 
YVhately’s  view  of  the  reasoning 
from  318  re.,  chiefly  confined  to 
moral  matter  318,  its  value  319. 

Exceptions,  becoming  numerous 


INDEX. 


417 


indicate  a faulty  classification  256, 
as  a means  of  refutation  329. 

Exceptional  Modals  78. 

Exceptive  Propositions  83,  easily 
converted  into  Exclusives  83,  in 
Syllogisms  151. 

Excluded  Middle,  what  97,  be- 
tween contradictories  and  subcon- 
traries 97,  a ground  of  affirma- 
tion 104. 

Exclusion,  as  a Method  of  Investi- 
gation 240,  two  forms  241,  its 
uses  241,  242. 

Exclusive  Modals  79. 

Exclusive  Propositions  83,  easily 
converted  into  Exceptives  83,  in 
Syllogisms  151. 

Experiment,  as  a means  of  investi- 
gation 224. 

Experimentum  crucis  273. 

Explicative  Modals  78. 

Exposita,  what  71. 

Extension,  not  predicable  of  time 
and  space  23  n.,  incompatible 
with  infinite  23  n. 

Extremes,  in  a categorical  Syllo- 
gism 108. 

Event,  in  the  calculation  of  chances 
what  165,  distinguished  from  a 
fact  214. 

Facts  defined  213,  distinguished  from 
Events,  Conceptions,  and  Ideas 
214,  phantasms  and  fancies  215, 
as  circumstances  215,  first  known 
as  complex  wholes  215,  distin- 
guished from  inference  230,  how 
used  in  Arguments  303,  distin- 
guished from  laws  303. 

Faculties,  University  distribution 
of  339. 

Fallacies,  defined  and  classified  182, 
in  form,  in  matter,  in  diction,  and 
extra-logical  183,  effect  of  183, 
Aristotle’s  list  of  them  184  »., 
Ignoralio  Elenchi  185,  Petitio  Prin- 
cipii  186,  Ambiguous  Middle  189, 
Division  and  Composition  190,  of 
Accidents  and  of  Quid  191,  post  hoc 
ergo  propter  hoc  259  n.,  Contradic- 
tio  in  adjectis  375,  Metabasis  379  n. 


Fancies,  distinguished  from  facts 
215. 

Faults,  distinguished  from  Fallacies 
183. 

Felapton  121,  reduced  to  Ferio  128. 

Ferio  119,  all  Syllogisms  beginning 
with  F may  be  reduced  to  127. 

Fesapo  121,  may  be  reduced  to  Fe- 
rio 127. 

P’estino  120,  may  be  reduced  to  Fe- 
rio 127. 

Figure,  of  Syllogisms  what,  and 
the  differentia  of  each  110,  the 
4th  Figure  valid,  though  unnatu- 
ral and  inelegant  111,  the  1st  and 
4th  depend  upon  the  same  prin- 
ciple 112,  the  2d  113,  the  3d  113, 
the  1st  has  six  valid  and  four  use- 
ful Syllogisms  119,  the  2d  has 
also  six  valid  and  four  useful  120, 
the  3d  Figure  has  six  121,  the  4th 
Figure  has  five  121,  the  2d  Figure 
proves  Analogy  by  affirmative  Pre- 
mises 124,  the  peculiarities  of 
omitted  in  general  discussion  130. 

Final  Causes,  what  31,  a basis  for 
Induction  313,  imply  a Creative 
Intelligence  314. 

Form,  distinct  from  the  matter  5, 
of  judgments  44. 

Formal  Properties  210,  imply  Mo- 
dal 222,  an  accidental  may  be 
formal  222,  the  basis  of  classifica- 
tion for  the  purpose  of  Induction 
249,  250,  the  basis  of  Analogy  as 
a Method  of  Investigation  258. 

Formula  7,  of  Classification  and  In- 
duction 146,  of  the  cumulative 
Argument  147. 

Fresison  122,  reduced  to  Ferio  128. 

General  Subject  in  instruction,  its 
division  360. 

General  Terms,  how  distinguished 
from  Collective  17. 

Genus,  a sphere  17,  predicable  in 
Quid  19  n.,  Summum  and  Proxi- 
mate 20,  what  may  be  predicated 
of  55. 

Giving  and  Conveying  words  of, 
how  to  be  interpreted  299. 


18* 


41 S 


INDEX. 


Goclknian  Sorites  140,  138  n. 

Goon,  the  Idea  of,  as  determining 
Methods  199. 

Hamilton  Sir  William,  his  new  Me- 
thod of  Notation  and  Quantifica- 
tion G7  n.,  see  also  Ike  Preface,  his 
Unfigured  Syllogism  111,  his  opii 
ion  of  Induction  308  n. 

History,  the  facts  of,  in  what  sense 
a field  for  Induction  311. 

Hypothesis,  what  218,  use  of  in 
investigating  modal  properties  223, 
in  general  226,  used  in  Demon- 
stration 288,  legitimate  use  of  in 
contingent  matter  289. 

Hypothetical  Judgments,  why  so 
called  45. 

Ideas,  furnished  by  the  Reason  11, 
which  determine  Methods  198,  dis- 
tinguished from  facts  214,  how 
transferred  from  one  mind  to  an- 
other 347,  of  Totality  370  et  seq. 

Identical  Judgments  48. 

Identity  of  objects  perceived  9, 
explained  33,  principle  of,  a ground 
of  affirmation  103. 

Ignoratio  Elenciii  not  a mistake 
in  Logic  185,  why  so  called  185, 
when  most  likely  to  occur,  and 
the  effect  of  185. 

Illicit  Process  of  the  Minor  and  of 
the  Major  115,  116. 

Immediate  Inference  explained  69. 

Immortality  of  the  Soul,  Bp  But- 
ler’s method  of  reasoning  about 
321,  334. 

Impertinent  matter  always  to  be 
rejected  367. 

Implied  Properties  209,  learned 
by  Observation  222,  by  Measure- 
ment 233,  by  Analysis  248. 

Impression  often  made  without  ar- 
gument or  Instruction  373. 

Improbability,  what  88,  not  the 
same  as  the  probability  of  the  op- 
posite 89,  nor  as  the  mere  want  of 
probability  90. 

Indifferentia,  what  properties  so 
called  20. 


Indirect  Conclusion  in  pure  cate- 
gorical Syllogisms  123,  must  he 
used  instead  of  the  direct  in  cer- 
tain cases  141. 

Individuals,  what  19,  absolute  and 
relative  27,  necessarily  included  in 
a Species  53,  what  may  be  predi- 
cated of  55. 

Individual  Judgments  60,  formed 
before  Universal  330  n. 

Indefinite  Judgments,  what  61, 
how  related  to  the  Negative  63'. 

Induction,  the  Formula  of  146,  as  a 
Method  of  Investigation  249,  Aris- 
totle’s definition  of  249  n.,  three 
classes  of  cases  251,  three  steps  in 
the  first  class  253,  second  class  254, 
third  255,  compared  with  Deduc- 
tion 276  ».,  as  a Method  of  Proof 
303,  implies  the  Uniformity  of  Na- 
ture 304,  and  a Creative  Mind  306, 
completed  into  Syllogism  308,  be- 
longs to  physical  matter  309,  does 
not  extend  to  accidental  proper- 
ties 310,  approaches  Demonstra- 
tion 311,  limited  to  properties  im- 
plied in  the  original  class-concep- 
tion 3 1 1 , by  means  of  Final  Causes 
313,  implies  an  Intelligent  Creator 
315,  how  far  applicable  316. 

Inequality,  comparisons  of  85. 

Inference  Immediate,  from  subal- 
terns 70,  from  universals  70,  from 
contradictories  70,  from  Exposita 
by  permutation  76,  by  the  sub- 
stitution of  terms  77,  from  judg- 
ments in  Necessary  Matter  211. 

Infima  Species  20. 

Infinite,  a term  in  Logical  Quantity 
23,  incompatible  with  extension 
23  n.,  meaning  of  the  word  36  n., 
in  Discrete  Quantity  39,  as  a Pre- 
dicate, how  proved  279. 

Intensity,  regarded  as  a cause  86, 
in  Syllogisms  155. 

Intensive  Quantity,  determined  by 
the  Comprehensive  60. 

Interpretation,  necessity  for  297, 
Rules  of  297. 

Intuitive  Judgments  106. 

Instruction,  Methods  of,  how  far 


INDEX. 


419 


belong  to  Rhetoric  347,  determin- 
ed by  the  conditions  of  conveying 
conceptions  348,  two  Methods  of 
362,  division  of  matter  in  refer- 
ence to  3G4,  order  in  366,  End 
as  determining  the  selection  and 
order  of  the  matter  367  et  seq. 

Investigation  the  method  of  find- 
ing Predicates  to  given  subjects 
219,  of  accidental  and  modal  pro- 
perties 222,  of  implied  223,  Modal 
by  means  of  hypotheses  223,  be- 
gins with  individual  objects  225, 
de  novo  and  following  another  226, 
use  of  hypotheses  in  226,  in  Dis- 
crete and  Continuous  Quantity 
232,  by  Average  237,  by  Exclusion 
or  Abscissio  240,  by  Analysis  243, 
by  Induction  249,  of  Causes  by 
Elimination  259,  leads  to  a first 
and  absolute  Cause  260. 


Jests  are  hut  ludicrous  classifica- 
tions 54. 

Judgment  7,  defined  43,  form  and 
matter  of  44,  scope  of  44,  of  three 
kinds  44,  Categoric,  Conditional, 
and  Disjunctive  44,  Hypothetical 
45,  Comparative  and  Probable  45, 
formation  of  47,  resolvable  into 
terms  and  terms  with  modals  47, 
Identical  48,  Individual,  Parti- 
cular, and  Universal  60,  quality 
of  Affirmative,  Negative,  and  In- 
definite 61,  Modality  of,  Problem- 
atic, Assertive,  and  Necessary  61, 
four  cardinal  A,  E,  I,  and  O 62, 
Negative  with  undistributed  Pre- 
dicates 67  n.,  every  judgment  im- 
plies another  69,  opposition  of  70, 
Permutation  or  contra-position  of 
71,  Comparative  84,  Probable  87, 
Conditional  91,  Disjunctive  97, 
Intuitive  and  Deductive  106,  An- 
alytic and  Synthetic  203,  in  Ne- 
cessary blatter  205,  a priori  and 
a posteriori  206,  when  incapable 
of  proof  277,  Individual  before  the 
Universal  330  n.,  Universal  ex  ne- 
cessitate rei  and  de  facto  330  n. 


Kant,  his  Categories  34  re.,  his  Syl- 
logisms of  the  Understanding  69. 

Lambert,  Iris  dicta  of  the  Figures 
124  n. 

Later-first,  a fault  in  Method  197. 

Latimer  Bp.,  his  exposition  of  the 
Fallacy  of  post  hoc  ergo  propter  hoc 
259  n. 

Law,  the  Faculty  of  339. 

Laws  restraining  liberty,  how  to  he 
interpreted  300,  distinguished  from 
facts  303. 

Length,  a secondary  property  23  re. 

Liberty,  laws  restraining,  how  to 
be  interpreted  300. 

Limits,  doctrine  of,  in  Progressive 
Approach  325. 

Loci,  what  219  re. 

Locke’s  classification  of  the  Sci- 
ences 340. 

Logic  defined  1,  later  than  Philoso- 
phy 1,  its  necessity  2,  holds  the 
second  place  in  Philosophy  3,  the 
science  of  deductive  thinking  3,  a 
Science  3,  in  what  sense  an  Art  3, 
its  relation  to  Rhetoric  and  Dia- 
lectics 4,  347,  not  to  he  regarded 
as  a means  of  discovery  4,  Formal 
or  Analytic  5,  Rational  5,  Applied 
6,  presupposes  a knowledge  of  the 
Matter  6,  proposes  no  new  way  of 
reasoning,  but  explains  the  old  6. 

Logical  Division  25. 

Logical  Quantity  22,  limits  and 
terms  in  23,  39,  of  three  dimen- 
sions 59. 

Major  Premise  in  categorical  Syl- 
logisms, what  108,  called  the 
“Principle,”  not  usually  expressed 
in  Induction  275  re. 

Major  Term  by  nature  and  by  loca- 
tion 108,  change  of  its  Modal  135. 

Material  Properties  209. 

Mathematics  deals  with  Concep- 
tions only  244  and  note. 

Matter  of  Arguments  5,  of  a Con- 
ception 14,  determines  its  Sphere 
15,  of  a Genus  and  of  a Species  21, 
accidental  21,  of  judgments  44, 


420 


INDEX. 


of  conditional  judgments  91,  as 
determining  Methods  202,  Neces- 
sary 204,  Contingent  205,  Neces- 
sary and  Contingent  in  the  same 
Conception  200,  Moral  212,  of  a 
Conception  divided  with  reference 
to  the  order  of  treatment  364,  im- 
pertinent to  be  rejected  367,  new 
matter  not  to  he  introduced  by  the 
critic  374. 

Maxims  210  n.,  how  distinguished 
from  Axioms  290  n. 

Measurement,  as  a Method  of  In- 
vestigation 232,  a means  of  inves- 
tigating implied  Properties  233. 

Mediate  Inference,  always  implies 
a Middle  Term  107. 

Medicine,  Faculty  of  339. 

Members  of  conditional  judgments 
91. 

Memory  depends  upon  Method  367. 

Metabasis,  fault  of  379  n. 

Metaphysics,  one  branch  of  Philo- 
sophy 3. 

Method,  included  in  Logic  1,  distin- 
guished from  the  Matter  and  the 
Form  of  Arguments  5,  Method  in 
general  194,  gives  unity  and  im- 
plies capacity  195,  order  implied 
in  196,  the  Ideas  that  determine 
198,  Matter  as  determining  202, 
of  Investigation  219,  Observation 
and  Testimony  223,  Measurement 
232,  Counting  and  Calculation  234, 
in  Mathematics  234,  Average  and 
Exclusion  237,  Analysis  243,  In- 
duction and  Analogy  249,  of  find- 
ing causes  (Elimination)  259,  of 
Proof  275,  Demonstration  281, 
Deduction  290,  of  appeal  to  Au- 
thority 293,  of  appeal  to  Facts  303, 
Induction  304,  by  Example  316, 
by  Analogy  319,  by  concurrence 
of  circumstances  322,  of  Progres- 
sive Approach  324,  of  Refutation 
328,  Direct  329,  Indirect  333,  In- 
direct Methods  always  imply  Di- 
rect Methods  to  the  same  result 
335,  Personal  336,  of  1 Historic 
determined  by  the  Idea  of  the 
Useful  347,  of  Instruction  for  the 


most  part  Rhetorical  347,  Ana- 
lytic and  Scientific  in  teaching 
359,  362,  of  Criticism  369,  how 
criticised  372. 

Middle  Term,  its  office  in  Syllo- 
gisms 107,  110,  must  be  once  dis- 
tributed 1 14,  the  law  of  changing 
its  Modal  134,  may  be  stated  indi- 
vidually 146,  the  necessity  for  so 
stating  it  147,  may  be  a disjunctive 
judgment  in  one  Premise  176,  am- 
biguity of  189. 

Mill  denies  the  reality  of  necessary 
matter  205  n.,  opinion  on  the  Uni- 
formity of  Nature  305  n. 

Minor  Premise  in  Categorical  Syl- 
logisms 108,  called  “ the  case,” 
“ the  example,”  or  “ instance,” 
109. 

Minor  Term,  by  nature  and  by  po- 
sition 108,  the  real  subject  of  the 
Syllogism  108,  change  of  its  Mo- 
dal 135. 

Modal  Properties  210,  investi- 
gated by  observation  222,  by 
means  of  Formal  Properties  223, 
225,  by  Induction  251,  252,  In- 
duction commencing  with  254. 

Modality  of  Judgments,  three  va- 
rieties of  61. 

Modals  77,  Explicative  and  Differ- 
ential 78,  Exceptional,  Exclusive, 
Conditional,  and  Protensive  79, 
when  omitted  and  when  inserted 
in  the  course  of  an  argument  132- 
135,  may  be  transferred  from  one 
term  to  the  other  136,  protensive 
Modals  in  Syllogisms  137. 

Modus  (aliens  and  ponens  172,  tollente 
ponens  and  ponenle  tollens  177,  po- 
nente  Wiens,  when  valid  in  disjunc- 
tive Syllogisms  178. 

Moods  oi  Syllogisms  115,  not  all 
valid  115,  116. 

Moral  Matter  212,  does  not  admit 
of  Induction  309. 

Multiplication,  a Method  of  Addi- 
tion 236. 

Name  of  any  thing  may  be  predi- 
cated of  that  thing  55. 


INI)  MX. 


±21 


Nature,  uniformity  of,  what  304, 
how  used  in  Induction  308,  ab- 
normal cases  in  316. 

Necessary  or  Apodictic  Judgments 

60. 

Necessary'  Matter  of  the  subject 
included  in  the  scope  of  the  Judg- 
ment 58,  in  relation  to  Method 
204,  Mill  and  Whe well’s  contro- 
Y’ersy  about  205  re.,  and  contin- 
gent in  the  same  conception  206, 
Analysis  of  245. 

Necessity,  Physical  and  Moral  212. 

Negative  Definitions,  ivliat  353  re., 
use  of  in  Instruction  365  re. 

Negative  Judgments,  what  61,  al- 
Yvays  distribute  the  Predicate  67 
and  note,  substitution  of  terms  in 
76. 

Negative  Terms,  complements  of 
the  Positive  36,  hut  few  37,  dis- 
tinction between  them  and  Priva- 
tive unimportant  37,  in  Discrete 
Quantity  38,  in  Continuous  Quan- 
tity 39. 

Non  tali  pro  tali,  Fallacy  of  188. 

Non  vera  pro  vera,  Fallacy  of 
188. 

Numerals  38. 

Numerical  Division  24. 


Oaths,  how  to  he  interpreted  299. 

Obiter  Dicta,  how  interpreted  302. 

Objects  of  Thought,  possible,  im- 
possible, and  real  12,  perceived 
as  wholes  47,  classified  as  soon  as 
we  have  more  than  one  221. 

Observation,  a Method  of  Investi- 
gation 220,  difference  between 
and  Testimony  221,.  as  a Method 
of  Investigation  223. 

Omission,  as  an  element  of  Method 
198,  not  testimony  229,  in  In- 
struction 368. 

Opinion,  as  distinguished  from  Truth 
217,  not  provable  by  Testimony 
296. 

Opposition  of  Terms,  relative,  con- 
trary, subcontrary,  and  contradic- 
tory 41. 


Order,  as  an  element  of  Method 
194,  196,  five  Canons  of  197,  of 
treatment  in  Instruction  361  et  seq. 
Ordinals  38. 

Ostensive  Reduction  of  Syllogisms 
128. 


Pantheism,  results  from  denying 
the  limited  nature  of  Positive 
Spheres  36  re. 

Pappus’  account  of  Mathematical 
Analysis  215  re. 

Parables,  how  to  be  interpreted 
301.. 

Particular  Judgments  60. 

Particular  Affirmative  Judg- 
ments distribute  none  of  their 
terms  68. 

Particular  Negative  Judgments 
distribute  their  Predicate  68. 

P arts,  Disparate  26,  assumed  as 
ivholes  26,  subordinate  26,  to  be 
criticized  only  in  relation  to  their 
Yvholes  372. 

Perception,  an  instantaneous  act  9. 

Permutation  of  Judgments,  what 
71,  by  means  of  Negatives  73. 

Personal  Refutations  336. 

Petitio  Principii,  Yvhat  1S6,  why 
so  called  186,  several  forms  of 
187,  188. 

Philosophy'  before  Logic  1,  neces- 
sitated it  1,  divided  into  three 
branches  2. 

Physical  Division  24. 

Plato  divided  Philosophy  into  three 
brauches,  2,  338,  his  use  of  the 
Yvord  “ Ideas”  311. 

Plausible,  the  Idea  of,  as  deter- 
mining Methods  199  re. 

Pleasure,  the  Idea  of,  as  determin- 
ing Methods  199. 

Porphyry,  his  account  of  the  Pre- 

■ dicables  17  re.,  19  re. 

Post  hoc  ergo  propter  hoc,  Fal- 
lacy of  259  re. 

Posit  to,  a Proposition,  what  172  re. 

Positiy'e  Terms  35,  imply  nega- 
tives 36,  in  Discrete  Quantity  38, 
in  Continuous  Quantity  39. 


422 


INDEX. 


Predicables  13,  as  reckoned  by 
Porphyry  17  Aldrich’s  account 
of  19  n. 

Predicate  7,  usually  placed  after 
tlie  Copula  4G,  used  with  refer- 
ence to  the  matter  of  the  Con- 
ception 47,  what  words  may  be  so 
used  47,  used  for  the  matter  of  its 
Conception  50,  must  include  the 
necessary  matter  of  the  Subject 
58,  matter  expressed  in  224, 
found  by  the  Methods  of  Investi- 
gation 219. 

Premises  in  Categorical  Syllogisms 
108,  both  negative  112,  the  rela- 
tion of  their  quantity  and  quality 
to  rest  of  the  Conclusion  108-117, 
affirmative  give  no  negative  Con- 
clusion 117,  their  order  unimport- 
ant 126,  one  sometimes  suppressed 
1 42,  a universal  may  not  be  sup- 
plied when  a particular  will  an- 
swer 143,  compound  in  Syllogisms 
149,  Premises  unduly  assumed, 
various  forms  of  188,  may  be  con- 
clusions of  preceding  premises  280, 
to  a Conclusion,  whatever  is  ne- 
cessary to  it  308. 

Primary  Properties,  their  relation 
to  the  Secondary  23  n. 

Privative  Terms  complements  of 
the  Positive  36,  used  instead  of 
Negatives  73. 

Probability,  its  nature  and  the 
method  of  estimating  it  87,  and 
improbability,  complements  of 
each  other  in  unity  88,  antece- 
dent 89,  exact  value  of  89,  ap- 
proximate 90,  general  and  special 
91,  dependent  162,  in  the  same 
and  different  events  165,  Alge- 
braic formula  for  its  computation 
170  n. 

Probable  Judgments  45,  87. 

Probable  Syllogisms  157,  method 
of  notation  in  160,  how  many  at 
least  160,  at  most  161,  when  the 
probabilities  are  dependent  upon 
each  other  162,  when  they  are 
independent  165,  methods  of  cal- 
culating 168,  169. 


Problematic  Judgments  60,  not 
used  in  the  Formulae  63. 

Progressive  Approach,  the  argu- 
ment of  324,  first  class  of  cases 
324,  second  class  325,  often  more 
satisfactory  than  Demonstration 
326. 

Proof,  how  different  from  Investi- 
gation 275,  Direct  276,  requires 
two  conditions  277,  Indirect  278, 
of  Negative  Predicates  278,  of 
Negative  Copulas  279,  Demon- 
stration 281,  Deduction  290. 

Properties,  what  13,  belong  to 
more  than  one  substance  13,  Es- 
sentia 17,  Differentia  18,  Acci- 
dental 19,  when  called  Qualities 
19  n.,  separable,  inseparable,  and 
individual  19,  as  primary  and 
secondary  23  «.,  material  and  im- 
plied 209,  formal,  modal,  and  va- 
riable 210,  not  distinguished  into 
kind  at  the  first  observation  but 
at  the  second  221,  Formal  first 
distinguished  222,  Formal  and 
Implied  not  distinguished  by  In- 
vestigation 222,  Implied  learned 
by  measurement  233,  by  analysis 
248,  of  classes  investigated  by 
Induction  251,  by  Analogy  257. 

Propositions  in  an  argument  7, 
contain  two  terms  and  a copula 
46,  permutation  of  71,  73,  con- 
version of  74,  simple  and  complex 
77,  Compound,  Express,  and  Im- 
plied 80,  with  Negative  Predi- 
cates, how  proved  278. 

Protensive  Modals  79,  their  effect 
upon  the  Formula  136. 

Protensive  Quantity  59. 

Pro-syllogisms  148. 

Psychology,  a branch  of  Philoso- 
phy 2,  some  knowledge  of  requi- 
site in  Logic  8. 

Qua,  as  indicative  of  alternate  con- 
ceptions 58  n. 

Quadrivium  the,  what  339. 

Quale,  predication  in  19  n. 

Qualequid,  predication  in  19  n. 


INDEX. 


423 


Qualities,  properties  when  so  called 
19  n. 

Quality  of  Terms  34,  of  Judgments 
61,  of  Propositions  changed  by 
means  of  Negatives. 

Quantity,  what  21,  of  three  kinds, 
Logical,  Continuous,  and  Discrete 
22,  of  terms  38,  of  judgments  59, 
of  three  dimensions  59,  and  three 
degrees  60,  in  conditional  judg- 
ments 96,  when  to  be  given  in 
Instruction  364. 

Question  distinguished  from  the 
judgment  43,  its  relation  to  the 
Conclusion  109,  mistaking  the, 
fallacy  of  185,  begging  the,  fallacy 
of  186. 

Quid,  predication  in  19  n.,  (dictum 
secundum  quid  ad  dictum  simpli- 
citer)  fallacy  of  191. 

Realities  of  Being  and  of  Truth, 
how  distinguished  12. 

Reasoning  from  Cause  to  Effect 
271,  called  also  reasoning  a priori 
271  7i.,  from  Elfect  to  Cause  272. 
See  Arguments. 

Recurring  Species  359. 

Reductio  ad  Absurdum,  as  a Me- 
thod of  Refutation  333. 

Reductio  ad  Impossibile  128,  may 
be  applied  to  all  Syllogisms  129. 

Reduction  of  Syllogisms  127,  os- 
tensive  and  ad  impossibile  128. 

Refutation  328,  three  Methods  329, 
Direct  329,  by  Exception  329,  of 
a Particular  Judgment  330,  of  the 
reasoning  instead  of  the  Proposi- 
tion 331,  Indirect  333,  Personal 
336. 

Relative  Judgments  45. 

Relative  Terms  of  two  kinds  40, 
imply  and  explain  each  other 
40. 

Religion,  Method  of  Investigation 
in  231,  proof  in  Matters  of  293. 

Remembering,  ease  of,  depends  upon 
Method  in  Instruction  367. 

Residual  Phenomenon  269,  how  to 
be  disposed  of  270. 


Rhetoric,  its  Methods  determined 
by  the  Idea  of  the  Useful  347. 

Scholastic  classification  of  the  Sci- 
ences 339. 

Sciences  become  more  deductive  as 
they  advance  292,  classifications 
of  338. 

Scope  of  Judgments  44,  what  pro- 
perties of  the  Subject  included,  in 
58. 

Secondary  Properties,  their  relation 
to  Primary  23  n. 

Senses,  the  external,  as  Means  of 
Investigation  224. 

Separable  Accidents  19,  not  in- 
cluded in  the  Scope  of  a Judg- 
ment 58. 

Sequence  in  Conditional  Judgments 
92,  may  be  stated  as  a Categorical 
Proposition  92,  of  various  kinds 
92-94,  complex  Sequence  94-95. 

Similarity  33. 

“ Some”  not  always  indicative  of 
an  undistributed  Term  64. 

Sophisms  or  Fallacies,  Aristotle’s 
list  of  184  n.,  of  Achilles  and  the 
Tortoise  235  n. 

Sorites,  the  usual  form  of  138,  the 
Goclenian  138  n.,  may  he  made 
from  any  Syllogism  139,  resolv- 
able into  Syllogisms  140,  cautions 
in  regard  to  their  formation  139. 

Species,  what  18,  predicates  in  quid 
19  n.,  Infima  20,  what  may  be 
predicated  of  21,  55,  parts  of  a 
Logical  Division  27,  Alternate  27, 
Recurring  359. 

Specific  Terms  35,  distributed  40. 

Spendthrift’s  Fallacy  191,  rather 
a fault  in  criticism  370. 

Sphere  of  Conceptions  14,  deter- 
mined by  the  Matter  15,  Coinci- 
dent and  Opposite  19,  Analogous 
20,  of  positive,  negative,  and  pri- 
vative terms  36,  37. 

Stewart  Dugald,  his  opinion  of  the 
classification  of  the  Sciences  340. 

Subaltern  Genera  and  Species  20, 
Judgments  70,  inferences  from 
70. 


4:24: 


INDEX. 


SUBCONTRARY'  JUDGMENTS  70,  may 
both  be  true  in  the  same  matter, 
but  not  both  false  71. 

Sdbcontkauy  Terms  41,  how  pre- 
dicable 42. 

Subject  7,  placed  before  the  Copula 
46,  used  in  reference  to  the  sphere 
of  the  Conception  47,  what  words 
may  be  subject  47,  used  with  re- 
ference to  its  sphere  50,  classified 
in  all  affirmative  judgments  54, 
distributed  in  universal  judgments 

68,  given  by  its  sphere  or  by  its 
matter  220,  general  and  individual 
in  Instruction  360. 

Subordinate  Divisions  26,  parts  26. 

Substance,  what  13,  must  have  se- 
veral properties  13. 

Substitution  of  Terms  in  affirmative 
propositions  76,  in  negative  77. 

Subtraction,  the  principle  of  236. 

Sufficient  Reason,  a ground  of 
affirmation  103. 

Syllogism  analyzed  7,  divided  into 
classes  106,  pure  categoricals  110, 
Canons  testing  the  validity  of  1 17, 
number  and  names  of  those  that 
arc  valid  and  useful  122,  their 
names  indicative  of  the  means  of 
their  conversion  126,  complex  ca- 
tegorical 131,  protensive  modals 
in  136,  compound  or  Sorites  138, 
any  Syllogism  may  be  expanded 
into  a Sorites  1311,  of  Modals  in 
131,  the  effect  of  protensive  quan- 
tity upon  136,  compound  proposi- 
tions in  149,  comparative  151, 
probable  157,  conditional  170, 
disjunctive  175,  not  a Petitio  Prin- 
cipii  186  and  note , material  and 
formal  378  n. 

Syllogisms  of  the  Understanding 

69. 

Synonymous  Terms  35,  may  be 
predicated  of  each  other  55. 

Synthesis,  what  216. 

Synthetic  Judgments,  what  203, 
a priori  and  a posteriori  206. 

Synthetic  Method  of  Teaching  359, 
362,  why  preferable  362,  based  on 
scientific  classification  363. 


System,  what  217. 

Technical  Terms,  how  interpreted 
298. 

Terms  9,  predicable  13,  acategore- 
matic  13,  concrete  14,  abstract  14, 
denotative  and  connotative  14, 
comprehension  and  intension  of 
14,  essential  and  modal  17,  gene- 
ral and  collective  17,  matter  of  21, 
synonymous,  equipollent,  ambi- 
guous, incompatible,  and  positive 
35,  negative  and  privative  36,  in 
discrete  quantity  38,  in  continu- 
ous quantity  39,  in  logical  quan- 
tity 39,  distributed  and  undistri- 
buted 40,  their  opposition  40,  re- 
latives and  correlatives  41,  anti- 
thetic 41,  contrary  and  sub-con- 
trary 41,  contradictory  41,  in  a 
proposition  46,  importance  of  their 
quantity  59,  distribution  of,  in 
judgments  64,  distributed  by  na- 
ture 65,  by  signs  65,  by  position 
67,  substitution  of  in  affirmative 
propositions  76,  in  negative  77, 
in  comparative  judgments  85,  in 
conditional  91,  in  disjunctive  judg- 
ments 98,  in  a categorical  syllo- 
gism 108,  definitions  used  for  131, 
the  modal  of  one  transferred  to 
another  136,  denoting  causes  264, 
force  of,  as  a basis  for  demonstra- 
tion 282,  criticism  of  375. 

Testimony'  distinguished  from  Ob- 
servation 221,  of  two  kinds  226, 
tests  of  its  value  227,  228,  229, 
must  be  positive  229,  negative,  of 
Yvhat  force  230,  in  necessary,  phy- 
sical, and  moral  matter  231,  to 
matters  resting  on*  authority  231, 
resolvable  into  observation  and 
authority  280,  legitimate  use  of, 
in  Natural  Sciences  295,  regarded 
as  a fact  322. 

Theology,  Methods  of  Investiga- 
tion in  231,  of  Proof  in  293. 

Theory,  what  217,  may  be  several 
for  the  same  facts  217. 

Thinking,  a primary  property  of 
mind  23  n. 


INDEX. 


425 


Thompson,  his  Outline  of  the  Laws 
of  Thought,  quoted  as  of  teaching 
an  un figured  Syllogism  111. 

Titles,  alternate  conceptions  of 
subjects  57. 

Topics,  what  219  re. 

Totality,  absolute  and  assumed  88, 
the  idea  of,  an  element  of  Criti- 
cism 370. 

Thicks  of  Rhetoric,  defined  192,  to 
be  distinguished  from  Argument 
in  Criticism  374. 

Trivium  the,  what  339. 

True,  the  Idea  of  the,  as  determin- 
ing Method  199. 

Truth,  when  a proposition  is  so 
called  217,  absolute  proved  only 
by  Demonstration  325. 


Undistributed  Middle,  Fallacy  of 
114. 

Undistributed  Terms  40,  their  re- 
lation to  Judgments  64-69. 

Unfigured  Syllogism  111. 

Uniformity  of  Nature,  what  307, 
how  used  in  Induction  308. 

Universal  Judgments  60. 

University  distribution  of  the  Sci- 
ences and  Faculties  339. 

Useful,  the  Idea  of'  determining 
Methods  199,  relation  to  the 
Beautiful  201,  determines  the 
Methods  of  Rhetoric  347. 

"T GTepov  ivpwTov , a fault  in  Method 
197. 

Usus  Loquendi  as  a guide  in  Inter- 
pretation 298. 


Validity  of  Syllogisms,  Canons  de- 
termining the  117. 

Variable  Properties  210,  may 
become  material  or  formal  210, 
not  properly  the  basis  of  classifi- 
cation 256. 

Volney’s  “ Ruins,”  cited  as  an  ex- 
ample of  fault  in  Method  333. 

Wells  Dr.,  his  discovery  of  the  cause 
of  Dew  271. 

Whately  Archbp.  his  account  of 
Analogy  249  re.,  his  account  of 
reasoning  a priori  271  re.,  from 
Example  318  re.,  his  “ Spend- 
thrift’s” fallacy  371. 

Whewell  Prof.,  his  controversy 
with  Mill  concerning  Necessary 
Matter  205  re. 

Whole,  the  Idea  of,  necessary  to 
Criticism  370,  by  what  deter- 
mined 371. 

Wholes  of  three  kinds  21,  as  Me- 
thods 372,  in  Arguments  how 
determined  375,  in  Investigation 
and  Construction  375. 

Witnesses,  their  character  and  po- 
sition as  affecting  the  value  of 
their  testimony  226. 

Words  denoting  Genera  used  with- 
out the  article  52. 

Zeno  the  Eleatic,  the  inventor  of 
Logic  2. 

Zoology,  cited  as  an  illustration  of 
the  two  Methods  of  Teaching 
363  re. 


THE  END. 


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FIRST  LESSONS  IN  ENGLISH  COMPOSITION. 

BY  G.  P.  QIJACKENBOS,  A.  M. 

12mo.  Price  45  Cent? 

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QUACKENBOS’ 

ADVANCED  LESSONS  IN  COMPOSITION  AND  RHETORIC. 
(nearly  ready.) 

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A DIGEST  OF  ENGLISH  GRAMMAR. 

BY  L.  T.  COYELL. 

12mo.  Price  50  Cents. 

This  work,  which  is  just  published,  is  designed  as  a Text-Book  loi 
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of  an  eminently  successful  Teacher,  and  will  be  found  to  possess  many 
peculiar  merits. 

At  a regular  meeting  of  the  Board  of  Education  of  Rochester,  held  June  13,  1853, 
the  following  resolution  was  unanimously  adopted: 

u Resolved,  That  Covell's  Digest  of  English  Grammar  be  substituted  for  Wells 
Grammar,  as  a Text-Book  in  the  public  schools  of  this  city,  to  take  effect  at  the  com- 
mencement of  the  next  school  year.” 

Extract  from  the  Minutes  of  a Regular  Meeting  of  the  Board  of  Education  of 
Troy,  May  31. s?,  1853. 

“Mr.  Jones,  from  Committee  on  text-books,  and  school  librarias,  moved,  that  Bul- 
lion's English  Grammar  be  stricken  from  the  list  of  text-books,  and  Covell's  be  substi- 
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From  forty-four  Teachers  of  Public  Schools,  Pittsburg,  Pa. 

“The  undersigned  have  examined  ‘ Covell's  Digest  of  English  Grammar,1  and  are  o< 
opinion  that  in  the  justness  of  its  general  \ ievvs,  the  excellence  of  its  style,  the  brevity,  ac- 
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From  all  the  Teachers  of  Public  Schools  of  the  City  of  Alleghany,  Pa. 

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mars now  in  use,  are  fully  satisfied  that,  while  it  is  in  no  respect  inferior  to  others,  it  is 
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schools  under  their  direction.” 

From  John  J.  Wolcott,  A.  M.,  Pr.  and  Supt.  9th  Ward  School , Pittsburg,  Pa. 

“ ‘ Covell’s  Digest  of  English  Grammar'  not  only  evinces  the  most  unceasing  labor,  the 
most  extensive  research,  the  most  unrclaxing  effort,  and  the  most  devoted  self-sacrificing 
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satisfactory  exposition  of  English  Grammar  that  has  come  to  my  notice.  It  appears  to 
me  that  every  youth  aspiring  to  become  master  of  the  English  language,  from  the  rudi 
mental  principles  to  the  full,  round,  beautiful,  faultless,  perfect  period,  will  make  this  vol 
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EXPOSITION  OF  THE  GRAMMATICAL  STRUCTURE  OF 
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BY  JOHN  MULLIGAN,  A H. 

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This  work  is  a comprehensive  and  complete  system  o English 
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From  Dk.  James  W.  Alexander. 

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English  language.  It  strikes  me  as  being  one  of  the.  most  valuable  contributions  to  this 
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Extract, from  a letter  from  E.  C.  Benedict,  Esq.,  President  of  the  Board  of  Educa- 
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“ I have  often  thought  our  language  needed  some  work  in  which  the  principles  of 
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able  and  appropriate  addition  to  the  works  on  the  language.” 

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designed  more  partieulary  for  minds  somewhat  maturer,  and  for  pupils  who  are  capable 
end  have  a deBire,  to  comprehend  the  principles  and  learn  the  philosophy  of  their  owe 
tongue.” 


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“ Reid’s  Dictionary  of  the  English  Language  appears  to  have  been  compiled  upon 
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be  found  excellent  as  a convenient  manual  for  general  reference,  and  also  for  various 
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GRAHAM’S  ENGLISH  SYNONYMS, 

CLASSIFIED  AND  EXPLAINED; 

WITH  PRACTICAL  EXERCISES.  DESIGNED  FOR  SCHOOLS  AND  PRIVATE  TUWSION 
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HISTORY  OF  ENGLISH  LITERATURE. 

BY  WILLIAM  SPALDING,  A.  M. 

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tion,  are  described  with  considerable  fulness  and  in  an  attractive 
manner.  In  the  subsequent  pages,  more  frequent  and  sustained  efforts 
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and  by  hints  as  to  the  theoretical  laws  on  which  criticism  should  be 
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The  manner  of  the  author  is  remarkably  plain  and  interesting, 
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nomena of  daily  experience,  and  the  interest  of  the  pupil  is  speedily 
awakened  by  the  consideration  that  Chemistry  is  not  a matter  belong- 
ing exclusively  to  physicians  and  professors. 

From  Prof.  Wit.  H.  Bigf.low,  Principal  of  Clinton  Street  Academy. 

“ The  eminontly  practical  character  of  the  Class-Book  treating  of  the  familiar  ap- 
plications of  the  science,  is  in  my  opinion  its  chief  excellence,  and  gives  it  a value  fin 
superior  to  any  other  work  now  before  the  public.” 

From  David  Syme,  A.  M.,  formerly  Principal  of  the  Mathematical  Department , 
and  Lecturer  in  Natural  Philosophy,  Chemistry  and  Physiology,  in  Columbia  Col 

“ Mb.  Youmans  : Df.ar  Sir, — I have  carefully  examined  your  Class-Book  on  Chem- 
istry, and,  in  my  opinion,  it  is  better  adapted  for  use  in  schools  and  academies  than  any 
other  work  on  the  subject  that  has  fallen  under  my  observation. 

“ I hope  that  the  success  of  your  Class-Book  will  be  proportionate  to  its  merits,  and 
that  your  efforts  to  ditfuse  the  knowledge  of  Chomistry  will  b«  duly  appreciated  by  the 
friends  of  education.” 

“Either  for  Schools  or  for  general  reading,  we  know  of  no  elementary  work  on 
Chomistry  which  in  svory  respect  pleases  us  so  much  as  this.” — Com.  Advertiser. 


“Youmans’  Chart  of  Chemistry”  accomplishes  for  the  first  time,  for 
chemistry,  what  maps  and  charts  have  for  geography,  astronomy,  geo- 
logy, and  the  other  natural  sciences,  by  presenting  a new  and  admir- 
able method  of  illustrating  this  highly  interesting  and  beautiful  science. 
Its  plan  is  to  represent  chemical  compositions  to  the  eye  by  colored 
diagrams,  the  areas  of  which  express  proportional  quantities. 


CHART  OF  CHEMISTRY. 


BY  EDWARD  L.  YOUMANS. 


ABOVE,  IN  ATLAS  FORM,  Nearly  Ready. 


18 


160  W754E 

Wilson 


250436 


Elementary  Treatise  on 
Logic 

DATE  I ISSUED  TO 

i ~ 


160  W754E 


<5o0436 


